A method of self--consistent fields is used to study the equilibrium configurations of a system of self--gravitating scalar bosons of spin--1/2 fermions in the grounds state without using the traditional perfect—fluid approximation or equation of state. The many--particle system is described by a second--quantized free field, which in the boson case satisfies the Lein--Gordon equation in general relativity, $\nabla_\alpha \nabla^\alpha\phi =\mu^2\phi$, and in the fermion case the Dirac equation in geneeral relativity $\Upsilon_\alpha \nabla^\alpha \psi = \mu \psi $(where $\mu = mc/h$). The coe~cients of the metric $\delta \alpha \beta$ are determined by the Einstein equations with a source term given by the mean value $\langle \phi \vert\tau_\mu\nu\vert \phi \langle$ of the energy--momentum tensor operator constructed from the scalar or the spinor field. The state vector $\langle \phi\vert$ corresponds to the ground state of the system of many particles. In both cases, for completeness, a nonrelativistic Newtonian approximation is developed, and the corrections due to special and general relativity explicitly are pointed out. For $N$ bosons, both in the region of validity of the Newtonian treatment (density from $10^-80$ to $10^54gcm^-3$, and number of particles from 10 to $10^40$) as well as in the relativistic region (density $\sim 10^54gcm^-3$, number of particles $\sim 10^40$, we obtain results completely different from those of a traditional fluid analysis. The energy--momentum tensor is anisotropic. A critical mass is found for s system of $N \sim $[(Planck mass)/m]$^2\sim 10^40$ (for $m \sim 10^-25$) self--gravitating bosons in the ground state, above which mass gravitational collapse occurs. For $N$ fermions, the binding energy of typical particles is $G^2m^5N^4/3 \hbar^-2$ and reaches a value $\sim mc^2$ for $N \sim N_crit \sim$ [(Planckmass)/m]$^3 \sim 10^57$ for $m \sim 10^-24$ g, implying mass $\sim 10^33$ g, radius $\sim 10^6$ cm, density $\sim 10^19g/cm^3$. For densities of this order of magnitude and greater, we have given the full self--consistent relativistic treatment. It shows that the concept of an equation of state makes sense only up to $10^42 g/cm^3$, and it confirms the Oppenheimer--Volkoff treatment in extremely good approximation.
There exists a gravitational spin--orbit coupling, but its magnitude is generany negligible. The problem of an elementary scalar particle held together only by its gravitational field is meaningless in this context.
$$N_crit \sim [Planck mass/m]^2$$
while for N fermions:
$$N_crit \sim [Planck mass/m]^3.$$

A. Ferrari and R. Ruffini."Theoretical Implications of the Second Time Derivative of the Pulsar NP0532'' \it Astrophys. J. Letters \bf 158, L71(1969).

Even in the early days of Pulsar Astrophysics it became clear that much information could be gained on the nature of these objects by analysing the change of their period. In particular, quite apart from sudden changes in the pulsar period ("glitches''), an analysis of the second derivative with respect to time of the pulsar period could give important information on the breaking mechanism of the rotating neutron star. In this work, which uses techniques of a low velocity approximation of relativistic theories, an analysis is made of the emission of gravitational radiation from rotating neutron star as being the possible consequence of asymmetries in the equatorial plane. The results from breaking are due to gravitational radiation and from breaking due to electromagnetic radiation from an offaxis magnetic field are compared and contrasted. Suggestions are also made for estimating the possibk lifetime of the Pulsar. We were able to confront these theoretical predictions with the results of Pulsar Timing. These results have allowed us to impose limits on the eccentricities of neutron stars in pulsars.

Remo Ruffini--Institute for Advanced Study, Princeton, New Jersey and John--Archibald Wheeler--Joseph Henry Laboratories, Princeton University, Princeton, New Jersey. "Relativistic Cosmology and Space Platforms''. ESRO Pub., A.F. Moore and V. Hardy. 1971.

Einstein's standard 1915 general relativity or geometrodynamics introduces a new dynamic participant on the scene of physics: geometry. Nowhere did the dynamics of geometry originally show up more impressively than in the expansion of the Universe. Today the role of curved space geometry, both static and dynamic, lends itself to investigation from space platforms or from the ground. or both, in many other contexts. Among those discussed here are: properties of a superdense or neutron star; pulsar physics; collapse of a star with big dense core to a superdense star in a supernova event or complete collapse to a black hole; physics of the black hole; galactic centers, jets, and quasi--stellar sources; gravitational radiation; Misner's mixmaster model of the universe; the primordial fireball radiation; the time--scale of the expansion of the Universe; the Universe as a lens, magnifying the apparent diameter of a far--away galaxy; the mystery of the missing matter; the formation of galaxies; reaching out via radiation receivers for more information on the physics of these phenomena; and finally the solar system itself as a testing ground for relativity including the traditional three tests of relativity; the retardation of light as it passes close to the Sun on its way to Venus and back; relativistic effects in planetary motion and searches via corner reflectors on the Moon for relativistic effects in the motion of the Moon, as predicted by Baierlein.

R. B. Partridge and R. Ruffini. "Gravitational Waves and a Search for the Associated Microwave Radiation'' . Gravity Research Foundation. Third Award. 12pp. 1970.

We discuss astronomical sources which might produce the pulses of gravitational waves reported by Weber (3). A fraction of the energy emitted by such sources may emerge as electromagnetic pulses associated with the reported gravitational events. We observe the galactic center at a favorable microwave frequency, 19 GHz. The directional sensitivity of Weber's detector (given below) is a maximum during our observing period, allowing a direct comparison between our data and his. If positive correlations are found, the propagation velocity of gravitational waves can be determined to one part in $10^11$.

R. Ruffini."Sources of Gravitational Radiation''. Invited talk, 30 minutes. New Orleans meeting of the American Physical Society.

This was the first invited talk given by R. Ruffini, and was presented at a meeting of the American Physical Society. During this meeting, W.O. Hamilton of Louisiana State University and W.M. Fairbank of Stanford University presented the research program for the super--cooled gravitational waves antenna. In his talk, Ruffini presented the first evidence for the possibility of detecting a large amount of gravitational radiation from material accelerated in the field of collapsed objects. This research program was developed and presented by him and his students and collaborators in further papers.

C.E. Rhoades, Jr. and R. Ruffini."Hagedorn Equation of State in Neutron Stars''. Astrophysical Journal Letters, 163, L83 . 1971

At a density of 5 x 10 gr/cm neutron star matter can be described by a system of three non--interacting degenerate gasses: electrons, protons, and neutrons. At densities 10 gr/cm and greater, strong interactions between particles can make significant contributions. At densities of 10 gr/cm, the production of new particles and resonances has to be taken into account. Under these conditions the equation of state proposed by Hagedorn, applies. In this work Rhoades (a graduate student of Ruffini's) and Ruffini have analyzed the effects of this equation of state in the computation of the equilibrium configuration of a neutron star. The authors, were able for the first time, to point out both the new effects of the "softening'' of the equation of state towards high densities and the "saturation'' of the value of the mass of the neutron star as a function of its central density, and as a consequence of the generation of the particles and resonances. A critical analysis of these results together with a study of the physical reasons originating from these results were presented by C. Rhoades in his doctoral thesis at Princeton University (advisor was R. Ruffini) and by R. Ruffini in his Les Houches lectures (see further).

R. Ruffini. "Emission of Gravitational Waves from the Pulsar. In the Crab Nebula''. Davies and Smith eds. H. Reidel. 1971

In this talk, given at the International Astronomical Union meeting held in Manchester in 1971, the author pointed out the relevance of the classical analysis of McLaurin, Poincare, Darwin, Jacobi and Jeans on the configuration of rotating fluid masses for the emission of gravitational radiation. Together with numerical estimates of the strength of the emitted radiation, the author presented evidence for the possibility of obtaining information on the internal structure of the neutron star from the existence of a large emission of gravitational radiation. The "signature'' of the gravitational radiation emitted in these processes was also examined.

R. Ruffini."Gravitational Waves''. Invited talk, 30 minutes, Particle and Field Section of the American Physical Society, Austin, Tx. 5.XI. 1970.

In this section, following an invited talk by J. Weber, Ruffini critically analyzed the energy problem connected with the explanation of Weber's events as being due to gravitational radiation bursts. This talk was based mainly on the theoretical work of Ruffini and Wheeler, leading for the first time to a rigorous analysis of gravitational wave detectors and their estimated cross--section.

R. Ruffini."Gravitational Collapse and Gravitational Radiation''. Invited talk, 40 minutes delivered at the International Astronomical Union general assembly in Brighton, England. 1971.

In this talk theoretical arguments were presented, which lead to the conclusion that the process of gravitational collapse is the only realistic source of conceivably detectable signals of gravitational radiation.

D. Christodoulou and R. Ruffini."On the Electrodynamics of Collapsed Objects''. Bulletin of the American Physical Society. Series II. 16, No. 4 612, 1971. Also reprinted (10 pages) in Black Holes, B. De Witt and C. De Witt. Eds. Gordon and Breach. 1973.

The details of the magnetic and electric field to be expected in a collapsed object nonradiative at $\infty$ ("Black Hole'') are here given. Also given are the formulae determining the maximum total energy extractable from a collapsed object and the definition of its angular velocity as seen from infinity. Physical meaning is given to the expression of the surface area. Typical order of magnitude of the preceding quantities for collapsed objects of different masses are here estimated.

This article proved to be popular and was written with the intention of communicating some of the major processes made in understanding the final configurations of collapsed stars to the largest possible audience. In this article, the authors summarized the results of their students' work with particular emphasis on the work of D. Christodoulou (graduate student of R. Ruffini's at that time) together with some of their most significant new results (see 3). Moreover, it was emphasized that of all the procedures for identifying a collapsed object in space at a great distance, the most promising consisted of analyzing a close binary system in which one member is a normal star and the other a black hole. The X--ray emission associated with the transfer of material from the normal star to the collapsed object would then be of greatest importance in determining the properties of the collapsed object.
This article has been reprinted many times and has been translated into many languages (Japanese, Russian, and Greek, among others). It has created much interest in the final configuration of stars after the endpoint of their thermonuclear evolution. The analysis of the possible processes leading to the formation of a black hole, via either a one--step process of a multistep process, was also presented for the first time in this article.

A formula is derived for the mass of a black hole as a function of its "irreducible mass'', its angular momentum and its charge. It is shown that 50\% of the mass of an extreme charged black hole can be converted into energy as contrasted with 29\% for an extreme rotating black hole.

Recent theoretical advances have clearly put in evidence that black holes are not only the only astrophysical objects that are fully describable by general relativity alone, but also to be the strongest storage of energy in the Universe. In this paper we give a new formula establishing for the first time the energetics limit of a black hole (50\% of the total mass energy can be extracted from a black hole!); we also give two new mechanisms of extraction of energy of unprecedented efficiency. We finally, shortly discuss the singularity problem in a realistic Black Hole.

This work is the first in a series of works completed by Ruffini together with his students (M. Davies and W. Haxton) and collaborators (F. Zerilli and J. Tiomno). Its aim is to analyze the processes of gravitational and electromagnetic radiation in extremely relativistic regimes by means of a fully relativistic analysis, starting with the Regge--Wheeler formalism. In this first work a direct integration of the Schrodinger -- like equation governing the emission of gravitational radiation was attempted, with a simultaneous search for two eigen values (phase and amplitude of the wave) in order to match the required bouindary conditions of purely outgoing waves at infinity and those at the horizon of the black hole. This work pointed out the the computations previously done by Ruffini and Wheeler in the slow motion approximation underestimated the total amouint of gravitational radiation emitted and in viewing the "global'' approach followed in the solution of the problem it was possible to conclude that the amount of gravitational radiation falling inside the black hole was in fact larger that the outgoing quantity at infinity. This work clearly indicated the possiblity of reaching the explicit numerical estimate of radiation processes by means of the Regge--Wheeler--Zerilli formalism and of leading to the development of powerful computational techniques for the solution of this type of problem (see following references ) .

We have comuted the spectrum and energy of gravitational radiation from a "point test particle'' of mass m falling radially into a Schwarzschild black hole of mass $M \gg m$. The total energy radiated is about 0.0104 $mc^2(m/M)$, 4 to 6 times larger than previous estimates; the energy is distributed among multipoles according to the empirical law $E_21- pole \sim (0.44m^2c^2/M)e^-21$ and the total spectrum peaks at an angular frequency $\omega = 0 .32c^3 / GM.$

This work gives the theoretical framework in which any electromagnetic perturbation F in a background field fixed by a Schwarzschild geometry can be expanded. The covariant maxwell equations are reduced to two linearly independent Schrodinger--like equations in the radial coordinate r. The angular dependence of the vector potential A is taken into account by expanding it in vector harmonics. The source term J is also expanded in vector harmonics and the final equations governing the evolution of this perturbation are analyzed. This work is analogous to the Regge--Wheeler--Zerilli gravitational perturbation analysis regarding electromagnetic perturbations, and gives the complete set of eigenfunctions in which an arbitrary ekctromagnetic field in the fixed Schwarzschild background can be expanded. This has generated further research and many new results, in particular, making it possible to compute the electromagnetic radiation emitted by a particle faning in a gravitational field (see further work by Ruffini). This work also represents the starting point for systematic inquires into an electromagnetic field situated in strong gravitational fields. It lead, above an, to further analyses by Zerilli, and a continued collaboration between Ruffini and Zerilli on the coupling of electromagnetic and gravitational radiation.

A complete relativistic analysis for gravitational radiation emitted by a particle in circular orbit around a Schwarzschild black hole is presented in the Regge--Wheeler formalism. For completeness and contrast we also analyze the electropmagnetic and scalar radiation emitted by a suitably charged particle. The three radiation spectra are drastically different. We stress some important consequences and astrophysical implications.

This set of works was presented at the April 1972 meeting of the American Physical Society. It summarized much of the work completed by Ruffini together with his students (M. Davis and D. Wilkins) and collaborators (L. Parker and J. Tiomno) during the academic year 1971--1972.

Using the approach of Israel, Wilson and Perjes we give the explicit form of the metric corresponding to two identical Kerr--Newman sources in equilibrium under their mutual electromagnetic and gravitational forces, with their spins oppositely oriented along a given axis. Symmetries, the complete analytic extension, the limit of infinite separation of the sources, and the two types of solution with vanishing separation are discussed.

In this paper, the case of the most stable electromagnetic structure--associated with a rotation sphere, which has a magnetic axis aligned to the rotation axis is discussed. Using a classical (non--relativistic) model it can be shown that the configuration that minimizes the total electromagnetic energy of the system is endowed with a non zero net charge. The importance of some of the implications regarding the physics of black holes is stressed, in particular, it is suggested that the fixed value of the magnetic ratio of a Kerr black hole is a direct consequence of a minimum energy condition. This last result is of the greatest relevance, since it stresses the possibility that black holes can be found in a binary system X--ray source and that they can be endowed with an electromagnetic structure. Much research is currently being carried out by J. Wilson in conaboration with R. Ruffini at Livermore, California using a direct numerical integration of a three dimensional hydrodynamical code.

The latest theoretical results are here analyzed and in the light of recent experimental discoveries the evidence is shown presented that X--ray sources and pulsars are different aspects of the same evolutionary process: gravitational collapse of a star at the endpoint of thermo--nuclear evolution. Estimates and detailed predictions for further experimental observations are given. The case is made that X--ray sources are the key objects that will (for the first time!) discriminate between a neutron star and a black hole. The importance of the X--ray sources as sources of gravitational radiation is presented.

An analysis of X--ray sources based on the Roche model is here presented. On this basis we can conclude that pulsating sources appear to have systematically smaner masses than nonpulsating sources. We suggest identifying the first objects as neutron stars and the second as totany collapsed objects or black holes. Detailed predictions are presented. Discriminating features between neutron stars and black holes are also given.

This book, with 329 pages of text and 80 pages of appendices, is considered tobe introduction to the field of relativistic astrophysics. It is mainly directed towards final year undergraduate and first year graduate students. The material ranges from an updated version of R. Ruffini's and J.A. Wheeler's "Cosmology from Space Platforms'' to a detailed analysis of cosmology covering topics such as the expansion of the Universe, the formation of the galaxies, the cosmological black body radiation, the missing mass, the large numbers and a final run down on the current knowledge (this final section is written by J.A. Wheeler).

Using the Regge--Wheeler-Zerilli formalism of fully relativistic linear perturbation in the Schwarzschild metric. we analyze the radiation of a particle of mass m falling into a Schwarzschild black hole of mass $M \gg m$. The detailed shape of the pulse of the tideproducing components of the Riemann tensor at large distances from the source are given as well as the angular distribution of the radiation. Finally, the analysis of the energy going down the hole indicated the existence of a divergence; implications of this divergence as a testing ground of the approximation used are examined.

On the basis of Einstein's theory of relativity, the principle of causality, and Le Chatelier's principle, it is here extablished that the maximum mass of the equilibrium configuration of a neutron star cannot be larger than 3.2$M_\odot$. The extremal principle given here applies as well when theequation of state of matter is unknown in a limited range of densities. The absolute maximum mass of a neutron star provides a decisive method of observationally distinguishing neutron stars from black holes.

We point out the existence of a generalized ergosphere in the Reissner Nortstrom geometry and we give an explicit formula to determine its range. These results are compared and contrasted with the ones obtained in the case of the Kerr solution. An explicit process of energy extraction from a Reissner Nordstrom black hole is given.

The details of the spectral distribution of the radiation emitted by a particle freely falling in gravitational field are given in the case of the most general static asympototically flat solution with regular horizon. No contradiction exists with the principle of equivalence. A clear enhancement of high multipoles is shown to exist.

The electric field generated by a charged particle at rest near a Scwarzschild black hole is analyzed using Maxwell's equations for curved space. After genralizing the definition of the hnes of force to our curved background, we compute them numerically and graph them with the charge at $r = 4M, 3M,$ and $2.2M.$ Particular attention is paid to the behavior of the lines of force near the event horizon and the smooth transition of the electric field to that of a Reissner Nordstrom black hole.

Gravitational radiation emitted by a particle projected with nonzero kinetic energy from infinite distance into a Schwarzschild black hole is examined. Direct comparison between a semirelativistic approach and the fully relativistic approach in the Regge--Wheeler--Zerilli formalism gives an insight into the nature of the results. Detailed spectral distributions are given. Contrary to the case in which the particle falls in with zero kinetic energy, the spectrum does not vanish any more at low frequencies and a considerably larger amount of radiation is emitted.

In "Black Holes''. Carter, Hawking, Bardeen, Throne, Novikov, Ruffini. Editors B. De Witt and C. De Witt. Gordon and Breach, 1973.

This was the nrst time such a large effort had been made to present a complete set of lectures on some of the basic aspects controlling the energetics of black hole physics. The lectures comprise four chapters and eighteen appendices.

In chapter one, a full survey on the physics of neutron stars is made, with a detailed analysis of the physical reasons leading to inevitable gravitational collapse. In chapter two, the electromagnetic perturbation in a fixed background is presented, together with details of the numerical techniques used in the numerical integration of the Schrodinger--like equations governing the radiation processes. In chapter three, the gravitational perturbations and processes of emission of gravitational radiation are described, including all technical details. A special mention is made of the analysis of the distinguishing features of gravitational radiation signals (polarization and spectrum). Finally, chapter four presents the energetics of black holes, mentioning in particular the mass formula of black holes and the energy extraction processes.

The only reason for inserting this work in the publication list is that it represents the accomplishment of a large organizational effort, started by Bernacca and Ruffini, that was directed towards the application of a system for observing pulsar--like phenomena in the optical, using the Astronomical Observatory of Asiago. This program has been started and is currently making important contributions to optical observations of binary X--ray sources .

This paper is based on the invited 1972 Joseph Henry Lecture of the Philosophical Society of Washington, which was delivered by Ruffini at the Cosmos Club on the 12th of May 19,2. It received the Annual Cressy Morrison Award in Natural Science for 1972 from the New York Academy of Sciences.

This paper was written for the Italian Encyclopedia of Science in order to explain to a large number of readers the great progress made in both the theoretical and experimental field of relativistic Astrophysics. A systematic survey of the major progress made in the classical testa for general relativity, as well as in the new test for leme thining effects in space technology, is presented. A section on the fundamental theoretical aspects of the physical of neutron stars and black holes is followed by a revies of the results of X--ray observations from the Uhuru satellite. Finally, the prospects for detecting gravitational radiation are discussed. A complete bibliography is also given.

This invited talk was delivered at a meeting in New York of the American Physical Society, and it is estimated that about 6,000 physicists attended. The evidence for identifying Cygnus XI as a black hole was summarized and the experimental evidence supporting the classification of binary X--ray sources advanced by Leach and Ruffini was discussed. Some of the major electromagnetic and energy properties of black holes discovered through the work of Ruffini and his students and conaborators were presented. Ruffini stated that:"since the discovery by Hubble of the expansion of the Universe, the observation of X—ray sources can be considered the greatest and most dramatic breakthrough in experimental relativity''.

For the case of high multiples we give an analytic form of the spectrum of gravitational and electromagnetic radiation produced by a particle in a highly relativistic orbit $r_0 =(3 + \delta) M $ around a Schwarzschild blacck hole of mass M. The general dependence of the power spectrum on the frequency in an three spin cases (s=O) for scalar, s=l for vector, and s=2 for tensor fields) are summarized by power $P \propto \omega^1-s \exp („2\omega/\omega_crit)$. Although they havo the common feature of an exponential cutoff above a certain frequency $\omega_crit = (4/\pi\delta) \omega_)$, where $\omega_0$ is the frequency of the orbit, the tensor case has a much broader frequency spectrurn than scalar or vector radiation.

A fully relativistic treatment is given to analyze the electromagnetic radiation induced by gravitational perturbations in extreme relativistic regions. For the sake of clarity, results are presented here for the simplest possible example: an uncharged mass m faning radiany into a field of a Reissner--Nordstrom solution. Explicit results governing the energetics of the process are found. The amount of the electromagnetic radiation radiated can be of the order of magnitude of the gravitational one.

We analyze the possiblility of neutrino enlission from matter accreting into a neutronstar member of a binary X--ray source. Estimates of the expected fluxes and neutrino energy are given for selected values of the accretion rate under the asumption that the neutrino production is mainly due to the reaction $\gamma \leftrightarrow e^- + e^+ \rightarrow v_e + \bar v_e$.

In this paper, some of the mathematical question encountered in solving the coupled system of equations governing the interaction between electromagnetic and gravitational radiation are examined. Iteration procedures, based on a generalization of Green's function technique, which Ruffini and his students used, is applied to this more colplex case, in which the presence of "feed--back'' terms is essential for interpreting the results. The numencal method presented in this paper can be applied to each and aL of the systems of equations of the kind considered here, and has remarkable properties of fast convergence.

The formula for the size at the generalized ergosphere given by Denardo and Ruffini for the Reissner--Nordstrom metric is shown to apply in complete generality to the case of any black hole. The structure of the ergosurface is discussed and analytic formulae are given for various asympototic limits.

Using a general relativistic treatment we have analyzed the coupled emission of gravitational and electromagnetic radiation in tile simplest possiible radiation process: a massive charged particle falling radially into a Reissner--Nordstrom geometry. Particular attention is given to a detailed analysis of the "feedback'': terms between gravitational and electromagnetic radiation.

In this detailed report of 75 printed pages, the theoretical aspects of gravitationany collapsed objects relecant to the physics of binary X—ray sources are reviewed with particular emphasis on the physical processes occurring in the field of black holes. This article summarizes much of the theoretical work on conapsed objects carried out by Ruffini and his students during the acadmeic year 1972--1973 at both Princeton University and Stanford University, while on leave. In both this talk and one given later at a meeting in San Francisco of the American Association for the Advancement of Science, the main issues concerning neutron stars and black holes and the latest prospects for experimental detection of gravitational radiation were discussed, and further clarification by future theoretical and experimental analysis was recommended.

Wilkins has pointed out that, in addition to the periodicities associated with circular orbits in the equatorial plane of a Kerr geometry, there exist periodicities connected with the longitudinal motion of particles. We extend this result ot spherical orbits of charged particles in a Kerr—Newman geometry. We give explicit examples of nonspherical orbits, illustrating dragging of inertial frames and these longitudinal periodicities. The relevance of these results for the physics of collapsed objects is discussed.

By considering a set of gedanken experiments we show how quantum mechanics imposes uncertainties of the mass, charge, spin, and multipole moments of a black hole. In the case of mass and charge the only limitations on the precision of the measurement arises from the size of the universe. However, in the case of the spin the limitations on the measurability arises from the intrinsic properties (horizon) of the black hole. The uncertainty in the spin is always larger than $\hbar/2$. It is shown how the mass, charge and spin of the black hole have to be considered as purely classical parameters deprived of any quantum property.

This talk was given at the annual meeting in Chicago in one of the most highly attended sections, namely, "New Physics in Galaxies''. The abstract of Ruffini's talk was entitled "The Impact of X--ray Astronomy'', an area of research unprecedented in the field of Astrophysics, which has enabled us, in a few years, to gain a deep knowledge of the latest stages in the evolution of stars in our galaxy. Moreover, information on the X-ray background gives new and important information on the structure and clusters of galaxies. From a purely theoretical view, the physics of collapsed objects has become one of the leading and most important topics of experimental Astrophysics. The experimental results obtained from objects ranging from neutron stars to black holes agree with some of the most advanced theoretical predictions. It also seems that in the near future we shan be able to detect "the moment of gravitational collapse''. In this talk great emphasis was placed on the study and analysis of short time variations in the X--ray signals, and on time scales to the order of a millisecond, such as with Cygnus XI.

In the Bulletin of the American Physical Society. 19, 94. 1974
This section of the A.P.S. chaired by S. Chandrasekhar, concentrated on the work of Ruffini's students cnd collaborators. It summarizes much of the work during the acadmeic year 1973--1974, bGth at Princeton and Stanford Universities.

At the annual meeting of the A.A.A.S. an entire section was organized by R. Ruffini and H. Gursky, entitled "Neutron Stars and Black Holes in the Universe''. The experimental aspects were presented by H. Gursky and the theoretical by R. Ruffini. In the final written version (150 typewritten pages) Ruffini traces the essential physical principles governing the late evolution of stars. Emphasis is placed on the fact that knowledge can still be gained from directly observing the process of gravitational collapse. This article, with a bibliography of more than one hundred references, completely reviews this field of research and indicates possible future developments.

The positive and negative root states ($E^+, E^- $) for a particle moving along a geodesic in a stationary background, introduced by Christodoulou and Ruffini, are here interpreted in the framework of a relativistic quantum field theory. It is shown how $E^+$ and $E^-$ have to be considered as the classical correspondent of the postive energy states of a quantized field. It is explicitely shown that crossing between the states $E^+$ and $E^-$ can occur and consequently the necessary condition for particle creation as given by Klein,Sauter, Heisenberg, and Euler can be encountered.

We examine the electromagnetic structure of a one--body solution of the coupled Einstein--Maxwell equations endowed with mass m, charge Q, specific angular momentum a and a parameter $l$. It is shown how the paramerter $l$ introduced by Newman, Tamburino and Unti is realted to thee magnetic monopole charge distribution of the solution. A relation is presented between the total mass energy of the system and its irreducible mass. The total mass energy can be much smaller that the irreducible mass. A general solution characrterized by the four parameters $m, Q, a$ and $l$ is here introduced.

In this paper the influence of a Schwarzschild black hole on a uniformly magnetic field is analyzed. The solution of Maxwell equations in a curved background offers explicit analytical expressions for the electromagnetic field tensor. The importance of this analytical solution arises from the way in which it renders possible an analysis of the structure of the lines of force near the event--horizon of the black hole. This problem is of the greatest interest for physics since in the physics of binary X--ray sources we expect to find a large amount of magnetic field carried by the accreting plasma. It is also clear that this work should only be considered a preliminary investigation of the highly complex problem of treating plasma accretion in relativistic magneto--hydrodynamics. This last program is currently being pursued by Ruffini and Wilson.

This article followed shortly after the discovery by J.H. Taylor of a binary pulsar, and offered some new possibilities for testing Einstein's theory of general relativity. An explicit evaluation is given of the Doppler and gravitational shifts to be expected in the pulsar period, as well as the magnitude of the periastron precession. A detailed explanation of how this system provides favorable conditions for measuring the gravitational spin--orbit coupling of the neutron star is given. The observation of this effect is not only a crucial test for general relativity, but also offers the possibilty of analyzing many properties of neutron stars and their beaming, which is due to the precession induced by the spin-orbit coupling.

Recent developments of relativistic astrophysics allow the observation of regimes in which all existing field theories have never been tested. In the description of these regimes, unreachable in any experiment performed in a laboratory on the Earch, our current knowledge of electrodynamics or elementary particle physics has to be extrapolated by many orders of magnitude. For the first time, we are able to observe phenomena in which fully relativistic treatment of gravitational interactions is mandatory.

Following the approach of Israel and Wilson and Perjes we give the explicit form of the metric corresponding to two Kerr--Newman sources in equilibrium endowed with opposite values of the Taub--Newman--Tamburino--Unti parameters. The two solutions have equally and oppositely directed spin vectors. The explicit structure of the electromagnetic fields is given for the case where the two sources are separate, and in the limit their separation goes to zero (coalescence). The asymptoic form of the metric is regular for $r \rightarrow \infty$; and when the separation of the two solutions is not zero the electromagnetic field asympototically approaches an electric monopole and a magnetic dipole field.

In this article a detailed analysis is made of the present status of theoretical and experimental work on the search for gravitational radiation. After an introduction, which details the theoretical framework and cross--section of gravitational radiation detectors, and analyzes the directivity and sensitivity to polarization of existing detectors, experimentally established upper limits of gravitational radiation fluxes are analyzed. The author then emphasizes the fact that the discovery of collapsed objects in our galaxy has changed every previous estimate and expectation in this field, and that now viable processes exist for creating gravitational wave detectors fall about 10 below the theoretically required sensitivity. The author summarizes the progress made in constructing a new family of super--cooled detectors.

This talk was given to an audience consisting mainly of elementary particle theorists and experimentalists. After presenting the recent progress on the observation and theory of binary X--ray sources, the talk was mainly directed towards recent progress on quantum ndd theories in curved space. After reviewing the results obtained by Deruene and Ruffini in their interpretation of the positive and negative root solutions arrived at by Christodoulou and Ruffini, the importance of the application of these results in interpreting the Klein paradox within the framework of general ralativistic treatment was mentioned. It was also explained that the main ideas in this talk were derived from the application of the classical works of Sauter, Euler, and Eeisenberg. In fact, an effective potential can be introduced which can at once account for the relativistic and centrifugal effects and those of the Coloumb interaction. The introduction of this effective potential anows us to treat the system as a purely classical system and then to apply the wen known procedures for evaluating the coefflcients of transmission. The importance of this analysis lies mainly in the procedure for obtaining an effective potential from a fully relativistic treatment rather than from a phenomenological point of view.

A comparison of electromagnetic radiation absorbed by a black hole and that emitted at infinity is made for selected circular orbits of a charged particle in a Schwarzschild geometry. Radiation intensity and beaming prjocesses for geodesic as well as ultrarelativistic unbound orbits are compared and contrasted with the special relativistic results of classical electrodynamics.

Following the classical approach of Sauter, of Heisenberg and Euler and of Schwinger, the process of vacuum polarization in the field of the "bare'' Kerr--Newman geometry is studied. The value of the critical strength of the electromagnetic fields is given together with an analysis of the feedback of the discharge on the geometry. The relevance of this analysis for this analysis for current astrophysical observations is mentioned.

In this talk the necessity of using a fully relativistic magneto—hydrodynamics in order to attack the problem of accretion into a black hole has been presented with the basic equation to be solved and a few examples of explicit solutions of greatest interest. In this talk the main idea presented was that the newly discovered gamma rays burst should be associated with the processes of accretion into black holes and due to processes of *ischarge a working in the magnetosphere of a black hole as a consequence of vacuum polarization (see pub. No. 57). A new program of theoretical research dealing with accretion into black holes and possible observational consequences has been outlined.

The crossing of the classical positive and negative energy states E+ and E-- introduced by Christodoulu--Ruffini and interpreted within the framework of a relativistic quantum field theory by Deruelle and Ruffini, leads to a Klein paradox. It has been shown bv Euler and Eisenberg that when the transmission coefficient T2 through the barrier between the E+ E-- states is small it is proportional to the probability of pair creation. Numerical computations show that, in the case of a small Kerr black hole ($GM/c^2 \leq \hbar/ \mu c$), the probability of pair creation of particles of mass $\mu$ is maximum when E h, where E is the energy of the created particles and M the angular velocity and the mass of the black hole.

By an explicit analytic solution, it is shown how in the accretion of a poloidally magnetized plasma into a kerr hole, a torque is exerted on the impalling gas, implying the extraction of rotational energy from the black hole. The torque arises from the twisting of magnetic field lines by the frame dragging effect. It is also shown how under suitable conditions, a sizeable charge separation can be found in the magnetosphere of accreting black holes and hence, an electric charge is expected to be induced on the black hole.

A textbook covering such fields as: pulsars, gravitational radiation, black holes, cosmology. This book will differ from the previous one by M. Rees, R. Ruffini and J.A. Wheeler, "Black Holes Gravitational Waves and Cosmology" in the sense that it will treat the arguments more thoroughly and in great detail so as to make the book readable by a larger number of students (senior, undergraduate, first year graduat students). It will also differ from the Les Houches notes by R. Ruffini, "On the Energetics of Black Holes", being a much more broad and extensive analysis without technical analytic details. The book is going to be pubilshed by Freeman of San Francisco and translation rights have alerady been assured by other European Companies.

A book in Italian published by Mondadori covering an in depth introduction to general relativity, the physics of neutron star and black holes and observational effects of general relativity.

By analyzing a relativistic quantized field in a classical background Kerr geometry resonance states with $\Gamma < 0$ (grouping with time) are found. The interpretation of these states is made in the framework of the effective potential approach previously introduced by Deruene and Ruffini. It is shown to be consequence of the interplay of the two processes of pair creation and resonance states in the field of a collapsed object.

A generalization of the classical approach of barrier penetration introduced by Klein, Santer, Heisenberg, and Euler to curved spaces endowed with future horizons is given. This technique allows one to recover most directly results obtained recently by Eawking. The treatment here presented encompasses, as special cases, the work of Deruene and Ruffini, of Damour and Ruffini, and of Nakamura and Sato.

Introduction: General Relativity and Black Holes.
Chap. 1: Cosmology and Physical Law -- "Specification'' and "generalization''.
Chap. 2: Einstein's Relativity -- "Special'' and "General''.
Chap. 3: Gravitational Equilibrium Limit of a Star and Compact Stars.
Chap. 4: Neutron Stars. Black Holes. and Binary X--ray Stars.
Chap. 5: Evaporation of Black Holes, Naked Singularities and others.

Some experimental results giving evidence for the observations both of neutron stars and black holes in our galaxy and some classical theoretical results in black hole physics are summarized. Recent advances in relativistic magnetohydrodynamics are then reviewed with special emphasis on the analysis of simple models leading to a better understanding of the properties of the magnetosphere of a black hole. The stability of the magnetosphere against processes of vacuum polarization is discussed as well as its relevance for possible sources of detectable signals of gravitational radiation.

The observation of binary X--ray sources have given new and important information about masses, the magnetospheres, and the energetics of gravitationally conapsed objects. We review some results on the energetics of black holes, on their stability, on their magnetosphere, and on process of vacuum polarization occurring in their strong gravitational fields. The theoretical interpretation of the many observations of neutron stars and black holes point to the possibility of probing, for the first time, the physics of extreme relativistic gravitational fields.

An analysis of perturbations in a curved background is developped fonowing the construction of Green's functions by the Hadamard's principal solution. Applications to numerical techniques are discussed.

Some experimental results giving evidence for the observations both of neutron stars and black holes in our galaxy and some classical theoretical results in black hole physics are summarized. Recent advances in relativistic magnetohydrodynamics are then reviewed with special emphasis on the analysis of simple models leading to a better understanding of the properties Or the magnetosphere of a black hole. The stability of the magnetosphere against processes of vacuum polarization is discussed as well as its relevance for possible sources of detectable signals of gravitational radiation.

After reviewing the Rhoades--Ruffini treatment for the determination of an upper limit to the numerical value of the critical mass of a neutron star, their numerical analysis of the equation obtained from the variational principle are criticany reexamined. Counter example are given for the application of the variational techniques. The absolute upper limit of 3.2 M to the critical mass of a neutron star is confirmed.

An extensive general review of the physical processes occurring outside the horizon of a black hole and their astrophysical relevance is presented. The major results of black hoks energetics, stability, vacuum polarization processes are reviewed in light of recent observation of X and Gamma Ray astronomy.

The necessary conditions for the trapping of charged particles by an electromagnetic field in the magnetosphere of a black hole are established. Three different regions are defined according to the rdative importance of electric and magnetic fields: regions of magnetic dominance, plasma horizons, lines of constant flux. Idealized models are used to illustrate the application of these criteria.

A book reviewing the technical capabilities of the spacelab -- Shuttle program and a set of authoritative reviews on the Astrophysics to be performed from spacelab.

A book reviewing the mathematical aspects of the Bianchi classification and application to Astrophysics in the framework of Einstein theory of gravitation. The observational consequency of Bianchi Universes are presented together with a new and in depth analysis of their singularity structure.

A model is presented analyzing accretion disks around black holes. Special attention is given to possible models with application suggested to SS433 and Bursters.

A new family of X--ray sources has recently been proposed including SS433. The general relativistic formula to fit the frequency dependence of the H/alpha lines in SS433 as a function of the phase is presented here. Particularly relevant for the verification of the model are the observations at the phase of minimum shift.

A relativistic equation, generalizing the Thomas Fermi Equation is given. A critical number of is found which is the electromagnetic analogue to the critical number against gravitational conapse.

The role of higher multipole (2) structures in the magnetosphere of puLsars is pointed out and explicit effects on the showing doux index are studied.

Some phenomenological consequences of the model presented in ref. 72 and 73 are developed and directly confronted with experiments.

We here introduce necessary conditions to be fulfilled in order to have stimulated emission processes in a gravitational field. We also define "regions of constant shift'' with respect to an asymptotic observer.

It is pointed out that degenerate massive neutrinos could from halos comparable in size and larger in masses than galactic structures.

The existence of a nonzero rest mass for neutrinos implies the possible existence of galactic size masses of degenerate self--gravitating neutrinos. We discuss some limits imposed on the masses of such systems by special relativity and cosmology.

Much progress has been made inrecent years on the knowledge of gravitationany collapsed objects thanks to a deeper understanding of relativistic field theories and to a large amount of experimental information obtained from x and gamma ray -- radio and optical astronomy [1]. Nevertheless, basic issues on the structure both of neutron stars and black holes remam unanswered.

The inverse scattering theory used by Belinsky and Zakharov for obtaining solitonic solutions of the Einstein equations is here applied to the case of a 5--dimensional space and interpreted in the framework of the Jordan--Kaluza--Nein theory. For two solitons exact, stationary, axiany symmetric and asymptoticany flat solutions are obtained.

In light of the current experimental tests of gravitational theories we have computed the masses of the equilibrium configurations of neutron stars within the parametrized post Newtonian formalism. It is also shown how general requirements like the conservation of, the energy and momentum of an isolated system do impose severe constraints on the P.P.N. parameters. Our results are at variance with those previously reported by Wagoner and Malone. An computations do also confirm the existence of a critical mass against gravitational collapse.

The structure of a gravitational wave burst emitted by a particle radiany imploding into a Schwarzschild black hole with a finite kinetic energy at infinity is analyzed in the framework of the Zerilli--Regge--Wheeler formalism. The three components of the burst a) precursor b) main burst c) ringing tail are analyzed and the results compared and contrasted with those obtained for a particle initially at rest at infinity. The ringing tail of the burst is studied in terms of the normal modes of a black hole.

A detailed review is presented of the theoretical models of the source of SS433 with special attention to ring models and processes of stimulated emission.

The 163.8 days period observed in the shifted lines of SS433 if due to Lense Thirring precession, should change with time as a consequence of matter accreting into the black hole and changing its singular momentum. The propagation of light signals within a few Schwarzschild radii of the black hole surface, in the ring models, may lead to the observation of further relativistic effects.

Expressions are given for the energy and momentum of a free particle in a Friedmann Universe and in an Einstein--Strauss Universe. Special attention is given to the determination of the conserved quantities for the particle motion. The necessary conditions are given for a particle injected into a Schwarzschild geometry from expanding open, closed or fiat dust--filled Friedmann Universe, matched to that geometry, to find itself in a bound orbit.

It is argued that the treatment of Muner and Rafelski on the relativistic Thomas--Fermi model is well known from the literature. Some basic differences between the screening of the nuclear charge due to a relativistic cloud of electrons in a neutral atom and the one due to vacuum polarization effects induced by a superheavy ion are discussed.

A Semi--relativistic treatment estimating the gravitational radiation emitted by a particle thrusted into a Schwarzschild black hole with a finite kinetic energy at infinity is presented making two extreme assumptions: (a) that the particle moves along a geodesic in a curved space and (b) that the particle radiates as if it were in flat space--time. The structure of the burst and beaming process of grantational radiation are studied. The merit of this approach lies in its simplicity and in providing a direct and complementary understanding of the results obtained by a fully relativistic treatment.

Galactic halos of massive degenerate neutrinos are analyzed for selected equilibrium configurations in which the central density of neutrinos is smaller than the density of galactic visible matter. On the ground of a simplified model some general conclusions are reached about the rotation curves of galaxies. These conclusions may be subjected to a direct experimental verification. The local neutrinos density in our galaxy may be as large as $10^7$ neutrinos $cm^-3$ .

Some of the most unique experimental features of the source SS433 are outlined as well as some implications of the theoretical models of this source.

The observations of the binary pulsar carried out by J. Taylor (1) have given the first evidence of the eYistence of grfavitaitonally radiation and further verifications of relativistic effects are likely to be performed on this astrophysical system (2). These considerations make this object one of the most interesting in the entire field of relativistic astrophysics.

Within the framework of a Gamow cosmology with massive neutrinos a scenario is proposed in which both galactic halos and globular clusters are formed due to the existence of a critical injection mass. Galactic halos are formed at red shift z 10-100 by self-gravitating neutrinos, and globular clusters at z 10 by a critical injection mass of primordial plasma (Gamow’s Ylem).

The growth of massive neutrino halos around a mass condensation in an expanding universe is considered using the simplified model of an Einstein—Straus universe. This model illustrates the possibility of capturing freely moving particles in a homogeneous and isotropic cosmological gas by the local gravitational field of a mass condensation. This capture process is particularly relevant to the neutrino background in a neutrino dominated universe and explicit formulas are given relating the maximum capture rate by a neutrino condensation to the cosmological redshift and the mass of the condensation. Analogies between self--gravitating systems of neutrinos in an asymptotically flat spacetime and the condensations which maximize the capture rate are noted and observational consequences are considered.

We derive a self--consistent solution to the problem of the gravitational equilibrium of a collisionless semi--degenerate Fermi gas. The treatment is applied to model massive halos observed on scales ranging from galaxies to clusters of galaxies, by means of nonzero mass neutrinos. A self consistent lower limit to the neutrino mass is derived for neutrinos to provide the dark mass on various scales in a lepton symmetric universe.

Two topics are discussed. The first one concerns the size, shape and stability of galaxies. Particularly, the massive neutrino halo theory is discussed to account for the missing mass of the galaxies. The second topic concerns SS433. An Attempt to analyze the peculiar characteristics of SS433 using a ring model is explained.

Galactic halos of massive fermions, of arbitrary half integer spin, or of massive bosons are considered. To give results of astrophysical interest, the fermions with spin s should have a mass $m \simeq 10eV/c^2/(2s + 1)^l/4$, while the bosons a mass in the range from $10eV/c^2$ to $10^-24eV/c^2$. We also consider galactic halos of more than one fermion species.

The distribution function of massive Fermi and Bose particles in an expanding Universe is considered as well as some associated thermodynamic quantities, pressure and energy density. These considerations are then applied to cosmological neutrinos. A new limit is derived for the degeneracy of a cosmological gas of massive neutrinos.

The values of the masses of the equilibrium configurations of neutron stars are analyzed within the framework of the standard nine--parameter post—Newtonian (PPN) theories of gravitation. The traditional approach imposes constraints on the PPN parameters via experimental tests. In this paper, further constraints on the numerical values of these parameters are imposed by basic conservation laws, such as the conservation of each component of the four--momentnm of an isolated system. As a consequence we are able to establish in the PPN formalism the existence of a critical mass for the equilibrium config- urations of neutron stars.

The nutation effects of an accreting disk around SS433 are analyzed within the framework of the fully relativistic mod of Fang and Ruffini.

Limits are established for the gravitational red--shift to be expected for galactic halos. The possibility that collapsed galactic halos have relevance in astrophysical systems is also advanced.

A Newtonian approach to the problem of the capture of particles by a gravitational condensation in a Friedmann universe is considered. Explicit formulae are given for the value of the momenta and injection angles leading to the capture, and a comparison is made with analogous fully relativistic results.

A method is presented to calculate the most general effects of the global anisotropy of homogeneous cosmological models of the angular distribution of the cosmic background radiation. Using a spherical harmonic expansion. Bianchi types I. V and IX are explicitly considered.

The influence of the visible matter of the galaxy on the galactic halo is examined in the two limiting configurations of a classical isothermal sphere and a fully degenerate configuration. We infer the masses of the particles composing the galactic halos. The possible role of dwarf spheroidal galaxies in probing the structure of the galactic halos at large galactic distance is considered.

On the basis of Bessel's classical papers De Media Aequinoctiorum Praecessione and De Nutatione compact formulae are given to interpret the observed vanations in the shifted lines of SS433 in terms of nutational and precessional effects of a disk in a binary system.

The nutational effects induced by a companion star on the emitting regions of SS433 are anlysed within the framework of the ring model. Analytic expressions are derived for the variations of the shifted lines due to the nutation of the disk; the amplitudes and periodicities of these variations are given. Constraints on the inclination angles and masses of the system are derived. These results are compared and contrasted with those of the "twin-jet'' model.

The influence of the visible matter of the galaxy on the galactic halo is examined in the two limiting configurations of a classical isothermal sphere and a fully degenerate configuration. We infer the masses of the particles composing the glactic halos. The possible role of dwarf spheroidal galaxies in probing the structure of the galactic halos at large galactic distance is considered.

Extending the tensor virial equations analysis we obtain new equilibrium solutions for inhomogeneous Riemann ellipsoids. It is shown that, taking into account anisotropic velocity dispersion and a confocal ellipsoidal density distribution, it is possible to find stable ellipsoidal figures of equilibrium, for which the existence of a massive galactic halo as a means of stabilizing the structure against bar--like modes of oscillation is not required. At the same time the arnount of velocity dispersion necessary in the model is not far from that actually observed in our galaxy. These results, obtained for specific values of the angular velocity, the vorticity and the axial ratios, naturally lead to triaxial galaxy configurations.

We show how within the theoretical framework of a Gamow cosmology with massive neutrinos, the observed correlation functions between galaxies and between clusters of galaxies, naturany lead to a "cellular'' structure of the Universe. From the size of "elementary cells'' we derive constraints on the value of the masses and chemical potentials of the cosmological "inos''. We outline a procedure to estimate the "effective'' average mass density of the Universe. We predict also the angular size of the inhomogeneities to be expected in the cosmological black body radiation as remnants of this cellular structure. A possible relation of our modd to a fractal structure is indicated.

The fact that the radiation of new particles of the fifth interaction from the binaries is much smaller than that of gravitation is shown by calculations. The radiation from a particle system with collision is also given.

The transition to the ground state for a system of self--gravitating bosons or fermions is examined. In the case of bosons, a phase transition of the first kind occurs, going from a classical to a fully condensed configuration.

We have derived a self--consistent solution to the problem of the stability of self--gravitating classical systems and applied the model to globular clusters and galactic halos. Our results, moreover, allow us to explain the existence of binary systems in globular clusters and fix an upper bound for the particle rest mass for galactic halos in the context of the massive neutrino hypothesis for the solution of the "missing mass'' problem.

Observed rotation curves for galaxies with values of the visiblc mass ranging over three decades together with considerations involving equilibrium configurations of massive neutrinos impose constraints on the ratio between the masses of visible and dark halo components in spiral galaxies. Upper and lower limits on the mass of the constituents of the dark matter are derived.

We introduce a general theoretical framework which imposes constraints upon the spin, masses, and phase space densities of the cosmological "inos'' forming the dark matter component of the Universe. The novelty of the approach is in using largely model--independent features of both galactic halos and cosmological thermodynamical equilibrium. Uncondensed bosons are excluded as a component of the galactic halos, while fermions are confirmed as best candidates. Explicit limits on the masses and occupation numbers of "inos'' fermions are established in terms of the masses and radii of galactic halos and of their cosmological abundances. Consequences on the associated cosmological background radiation are given.

This volume presents a detailed survey on the theory of the creation of the Universe. It comprises reprints on subjects related to the development of quantum cosmology. As an introduction to the subject, an overview of quantum cosmology is included in the first chapter of this volume.

Within the theoretical framework of a Gamow cosmology with massive "inos'', we show how the observed correlation functions between galaxies and between clusters of galaxies naturany lead to a "cellular'' structure for the Universe. From the size of the "elementary cells'' we derive constraints on the value of the masses and chemical potentials of the cosmological "inos''. We outline a procedure to estimate the "effective'' average mass density of the Universe. We also predict the angular size of the inhomogeneities to be expected in the cosmological black body radiation as remnants of this cenular structure. A possible relationship between our model and a fractal structure as indicated.

On the basis of red--shifted statistics of collisionless gas, the properties of decoupled cosmological boson are derived. The equations of states are considered for the various decoupling epochs and they are different from classical Bose gas, particularly, in the case of bosons which decoupled at their relativistic regime. The cosmological limits on the mass of boson are also considered.

We consider the possibility that galactic structures be formed bv successive fragmentations in the still expanding phase of the Universe. This point of view in contrast with the traditional approach of "pancake'' theory. We here study the initial density contrast for fragmentation as well as the development of successive fragmentation process within a given fragment.

Within the framework of a self--similar observer--homogeneous model, a Mandelbrot's fractal, the observed amplitudes of the correlation functions for galaxies, clusters and superclusters are expressed by a simple analytic formula as function of the fractal dimension and a simple size. The various discrepancies among the observed correlation functions are naturally resolved in terms of appropriate normalizations.

The observational data on the amplitude of the correlation function of galaxies in the direction of the Coma cluster are confronted with analytic formula derived for a self--similar observer--homogeneous structure.

It is shown that the spatial two--point correlation functions for galaxies, clusters and superclusters depend explicitly on the spatial volume of the statistical sample considered. Rules for the normalization of the correlation functions are given and the traditional classification of galaxies into field galaxies, clusters and superclusters is replaced by the introduction of a singe fractal structure, with a lower cut--off at galactic scales. The roles played by random and stochastic components in the galaxy distributon are discussed in detail.

We discuss some inconsistencies in a recent letter by Vicsek and Szalay.

We present a new class of anisotropic inhomogeneous models of elliptical galaxies based on the McLaurin and Jacobi--Dedekind sequences of `Papuru' ellipsoids. These models are mantained in equilibrium either by the rotation of the figure (i.e. of the potential), or, alternatively, by stellar streaming with respect to the figure, which is fixed in space. The only hypothesis on the density distribution is that the equidensity surfaces are similar concentric ellipsoids.
Both triaxial and spheroidal equilibrium solutions are found, with a varietv of geometrical and dynamical configurations. The stability of equilibrium systems against global oscillations is tested under particular assumptions on the behaviour of the velocity fields.
We find that the triaxial configurations are in general energetically favoured with respect to the spheroidal ones, giving a new argument in favour of the triaxiality of elliptical galaxies.
From the observational limits on the ellipticities of galaxies, we deduce rather strict limits on the anisotropies of real systems, and, consequently, on the main physical properties involved.
We also show that, if triaxiality is a common characteristic of elliptical galaxies, the compresence of figure rotation and stellar streaming is a dynamical condition necessary for the equilibrium of galactic structures characterized by the observed $V/\sigma$ values.

This is the sixth of a series of papers that examines the possible role of massive and weakly interacting fermions as constituents of galactic dark halos. In paper III of this series we have studied the possibility that the observed flat rotation curves of spiral galaxies are due to the presence of an halo composed by fully degenerate fermions. In two other papers of this series (papers IV and V) the structure and the stability of self gravitating isothermal conngurations composed of classical or semidegenerate fermions have been investigated. A cutoff in the phase--space distribution of the particles has been introduced in order to avoid the problems that arise from the unfiniteness of isothermal configurations as usually described. In this paper we have considered the implications of the same semidegenerate configurations with a phase--space cutoff in presence of a visible matter component. The comparison of these theoretical analisys with the observed data on the rotation curves of spiral galaxies allows us to impose upper and lower limits on the mass of the particles that compose the dark halos and to obtain informations on the ratio between the masses of the dark and visible matter. We have also given the analytical dependence of the above limits on the degeneracy parameters of the halo special in the limit of classical configurations. We compare and contrast the results with the ones obtained in paper III for fully degenerate configurations.

The odd modes stability analysis of S--type Riemann ellipsoids generalized to an autosimilar density distribution law and an anisotropic pressure tensor is performed in the framewwork of the tensor virial theorem.

We apply the tensor viral theorem to the analysis of a new class of anisotropic inhomogeneous models for elliptical galaxies. The models are characterized by simultaneous rotation of the figure (potential) and internal streaming motion. A very general density distribution is assumed, with concentric similar (generally triaxial) ellipsoids as equidensity surfaces. The anisotropy is parametrized by the ratio of the mean velocity dispersion in the plane of rotation to the component along the rotation axis. We give detailed analysis of the relevant physical properties of the models, as the total kinetic energy, the angular momentum, and the total energy. We show that, one one axial ratio is fixed, the minimum energy configuration is triaxial one. The equilibrium shape turns out to be determined by the ratio of the internal streaming to the figure rotation X, together with the anisotropy . By plotting our equilibrium sequences on the ($\epsilon, V/\sigma$) plane, we try an interpretation of the observed positions of eniptical galaxies on this plane in terms of X and ,$\beta$. Our main conclusions are: i) the anisotropy in elliptical galaxies is restricted in a relatively narrow range around the isotropic value; ii) triaxial ellipticals must be characterized by the simultaneous presence of figure rotation and internal streaming motion, in the opposite sense. As an example of application of the models, we analyze the gross properties of a particular object (NGC 5266,, finding a remarkable agreement with a previous, more detailed, study.

The de Vaucouleurs astrophysical desnity--radius relation in reinterpreted in the framework of the fractal structure of the Universe in presence of a lower and upper cut--off size.

We study the anisotropies of the cosmic background radiation within the framework of a recent model which considers a fractal distribution of cosmic matter up to characteristic cells of size 100-300 Mpc. This model, while it meets no diffculty with anisotropy data at angular scales $\gamma < 1^\circ$, is usefully constrained by data at $1^\circ < \gamma < 90^\circ$. We impose limits on the rms perturbation amplitude at thermal decoupling, which depend on $\gamma^*$, the angular size of the fractal cell. A recently claimed detection of anisotropy at the scale of 8$^\circ$ is also discussed in the light of the model.

We examine the case of Lee and Weinberg leptons with a non--vanishing chemical potential and, correspondingly, we establish the cosmological limits on the relative lepton number $\beta$ and the masses of the inos. In order to have a flat universe the relative lepton number is bounded to the $\beta_crit \leq 1.6 \cdot 10^-9$.

We give a naive derivation of Berry of photon travelling along opticalifibre and its Sagnac facto, which differs from the original treatment of Chiao and Wu. In addition a new factor unknown before appears, it must become significant in a strong gravitational field suc as one surrounding the Kerr black hole.

We compare and contrast recent results we have published on a finite system of isothermal selfgravitating particles with the one obtained by Zel'dovich and Podurets.

We examine the relativistic and Newtonian configurations of a system of classical particles with a distribution function with a cutoff in the momentum space. These distributions are obtained as classical limit of more general quantum statistics. The characteristic physical quantities of astrophysical interest of the equilibrium configurations are given, assuming selected values of the parameters. The stability of these configurations is treated both from a global point of view of the mass--central density and mass--radius relation as well as by introducing the concept of an effective polytropic exponent. The results are compared and contrasted with the existing ones in literature.

The distortions in Hubble ratio by density inhomogeneity in the universe are calculated for different models within an elennentary cell. The extrapolation procedure for global Hubble constant and other quantities are discussed. It is shown that such distortions have great theorethical and observational significances in density distribution, clustering prperty, large scale peculiar velocity field, and the estimation of the mean density parameter.

We examine the spectrum of cosmological perturbations which may give origin to a cellular observer--homogeneous self similar structure in the Universe, which we have recently proposed. We assume that this structure originates by successive fragmentations in the dark matter "ino'' component, due to a process of Jeans instability. The fragmentation is characterized by the number of fragments (N) occurring at each step and by a characteristic "lagging time factor'' ($\tau$) at each successive fragmentation. In order to fulfil the observed spectrum of perturbations, at the present epoch, suitable values r are defined, the process is quite independent on the value of N. The initial spectrum of perturbations is found to have a flat Zel'dovich spectrum with an upper and lower cutoff. The initial amplitudes of the perturbations, as well as the ones to be found at the era of decoupling between matter and radiation, are discussed.

The de Vaucouleurs mass density relation is interpreted in term of a fractal and cellular structure and the usually adopted cosmological conditions of homogenity and isotropy, on the three dimensional space, are critically discussed.

Under eikonal approximation on Maxwell equation in curve space, the spin function of photon in degenerate metric is determined. Furthermore, we present an investigation of phase factor that photon may receive in Kerr geometry.The resulting phase factor consit of two parts, real and image one . The real part has been interpreted as making the rotation of polarization plane for linear polarized light, and irnage one make the light intensity descreasing along with photon propagating in gravitation field. Finany, so caned "Sagnac factor'' concerning with phase shift is given.

For the dominant component of the dark matter which dominates the matter of the Universe, the weakly interacting neutyral leptons are discussed. The cosmological rate equation for leptions with non--zero chemical potentials are solved and new cosmological constraints on the mass and degeneracy paramter are obtained. For light leptons, the formation of large scale structure of the Universe were discussed in the framework of the fractal set.

We analyze with a general relativistic treatment the configuration of a quantum system of fermions with a distribution function with a cutoffin momentum space. This distribution function also introduces a spatial cutoff in selfgravitating systems otherwise unlimited. The quantities of astrophysical interest of the equilibrium configurations are given for selected values of the parameters from the classical nondegenerate limit to the quantum fully degenerate limit.

An alternative interpretation of Peebles and co--workers' results on the angular two--point correlation amplitude of galaxies in the Zwicky and Shane—Wirtanen catalogs is here presented, supporting the idea of a large--scale structure of the Universe consisting of 110--200 Mpc fract.31 cells.

A system of N self--gravitating bosons or fermions can, by loss a total energy, concentrate, gain gravitational energy, and heat up. If the particle number N is smaller than a critical number $N^F_crit \sim (Planckmass/m)^3$ for fermions and $N^B_crit \sim(Planckmass/m)^2$ for bosons, the system can heat up to temperatures and concentrate to densities such that some particles win reach a quantum ground state, functional of the total particle number. By further cooling of the system, the N particles approach well--known fully condensed or fully degenerate configurations. For bosons the apperance of a quantum condensed state leads to a phase transition of the first kind. For $N > N^F_crit$ fermions $N > N^B_crit$ bosons, the system increase their temperature and condense to configurations for which a general relativistic treatment is mandatory. The concept of maximum temperature for a self-gravitating Bose and Fermi system is introduced.

A lot of observational evidences on the distribution of matter in the Universe at its various hierarchical levels--galaxies, clusters of galaxies, superclusters --seem to suggest strongly that it may be succesfully described by using a fractal approximation in the range of sistances from some fractions of Megaparsec to some hundreds of Megaparsec. One evidence is based on the spatial two--point correlation functions for the various galactic structures. Once the appropriate self--similar scaling relation is taken into account, it is easy to recognize that an the hierarchical levels of distribution of matter are in fact part of the same fractal structure. In this context we give some rules for the correlation analysis $^3,7)$. Another kinc: of proof for the fractal interpretation is the work by de Vaucouleurs $^14,15)$ where it is shown how the density versus radius relation for the matter in the Universe scales as an inverse power law form with an exponent very similar to the one satisfied by the correlation function. Once an appropriate value for the galactic mass is considered$^18)$ it is easy to see how the de Vaucouleurs results agree with the correlation function analysis in a neutrino dominated fractal cell model for the Universe $^19)$.

The triaxial equilibrium figures of rotating inhomogeneous ellipsoidal configurations with a density distribution stratified on similar ellipsoids, a mean streaming motion linear in the coordinates and an anisotropic pressure tensor (here referred to as "anisotropic S--Type Riemann ellipsoids'') are analyzed in the framework of the tensor virial theorem. The equilibrium solutions are first represented by the values of the anisotropic pressure parameters consistent with a given ellipsoidal figure. The analogous of the classical Riemann equilibrium sequences are defined and the Dedekind's theorem is generalized to this contest. The equilibrium figures are then depicted given the axial ratios compatible with a given value of the anisotropy. A stability analysis of the equilibrium is performed against odd mode second harmonical pertubations in the configuration space. Merits and limits of this approach to modelling eniptical galaxies are discussed.

An alternative interpretation of the observational results on the angular two-point correlation functions is here presented. They are used for determining the upper cutoff $R_co$ of a cellular structure for the Universe, each cell being a fractal, but randomly distributed with respect to the others. The values obtained seem to support the above scenario, even if further analyses are needed.

We present here an investigation of phase factor that photon may receive in a rotating frame of reference. The resulting pjhase include the three part, the Berry phase, the Sagnac factor and a new term unknown before. The new phase factor is due to the coupling of intrinsic spin of photon with rotation, an must became significant in a strong gravitational field produced by a rapidly rotating object. The experimental justification of the new effect is suggested.

It is shown the highly inhomogeneous self--similar distribution of extragalactic objects, put in evidence bv observations on spatial and angular correlation functions of galaxies, clusters and superclusters up to scales of about 100 Mpc, have been conciliated with the dominant homogeneity and isotropy of the Large--Scale Universe.

In t\his paper we analyze the equilibrium, the stability and some physical properties of a class of spheridal configurations discovered in the framework of previous studies on anisotropic and inhomogeneous ellipsoidal system. The systems studied here are oblate spheroids which rotate perpendicularly to the symmetry axis. We take into account the inhomogeneity of the density distribution, the anisotropy in the velocity distribution as well as two types of global motions: figure rotation and internal streaming. The method of analysis is the solution of the tensor virial equations and their second order perturbations.The requirements of equilibrium and expecially of stability put strict limits on the possible range of ellipticities and anisotropies of these systems. Such systems can in fact exist only if other components and only if the axial ratio is greater than $\sim$ 0.1.We find also that there is a maximum and minimum angular velocity, at which the potential (figure) can rotate.

The problem of statistical properties of neutral plasma type configurations (systems of N charged particles) is considered. The criterion of relative instability of many--dimensional dynarnical systems proposed in [5] and based on the calculation of the Ricci curvature in the direction of the velocity of geodesics in the configurational space is used. Two kinds of numerical experiments are performed in order to investigate: a) relative instability of different static configurations; b) variation of instability properties during the evolution of a given system.
The results of calculations enable us to understand the dependence of instability properties of systems on their physical characterics. The method used here can be applied to more complicated systems -- plasma configurations of physical and astrophysical interest.

A rigorous treatment of the violent relaxation phase of a large self--gravitating stellar system is made in the framework of the analytical dynamics. In the regime in which the coarse--grained virial theorem can be applied, the stellar system can be considered a \it mixing system. The consequent instability of the Anossov flow leads to the evaluation of the violent relaxation time scale.

We indicate some possible astrophysical of the Riemann ellipsoids ( S--type and I--type, according to the classification made by Chandrasekhar) in two very different regimes: (a) in the dynamics of an isolated elliptical galaxy and (b) in the phases of a newly formed neutron star.

The S--type Riemann configurations are generalized to a non--linear form of the velocity field, given by a polynomial expression in odd powers of the coordinates. The velocity field with a cylindrical structure and the equilibrium equations are given. The adjoint solutions, in the Dedekind sense, have been found and discusses. Finally the equations for the stability against odd and even modes of perturbations are presented and the general algoritms for the solution of the characteristic equations are given.

A general expression of two-point angular correlation function $\omega(\theta)$ is presented for the cellular fractal structures. The background contribution to $\omega(\theta)$ of the cellular distribution is fully considered in our derivation. A critical discussion about how to use the results presented here to test theoretical models is given.

The Dirichlet problem concerning the equilibrium conditions, under which a selfgravitating homogeneous fluid mass can maintain at every instant an ellipsoidal form, is here generalized. We provide the conditions necessary to solve the Dirichlet problem in a more general case of heterogeneous masses having nonlinear internal motions, using the second--order virial equations. The conditions for the stability are presented. It is also proved that the Dedekind theorem generalized to these new solutions is valid. These models may lead to a direct explanation of some basic features of galactic morphology.

The well--known Dirichlet problem defining the ellipsoidal equilibrium configuration for a self--gravitating homogeneous fluid mass endowed with internal motion linear functions of the coordinates is here generalized. In the present work using the second--order virial equations we provide the conditions necessary to solve the Dirichlet problem in a more general case of heterogeneous masses having nonlinear internal motions. The equations for the stability are presented with the general algorithms for their solution. The generalization to these new solutions of Dedekind's theorem is also proved. These models may lead to a direct explanation of some basic features of galactic morphology. \ item (171) See no. 163

We study the anisotropies of the cosmic background radiation within the framework of a recent medel which considers a fractal distribution of cosmic matter up to characteristic cells of size 100--300 Mpc. This model, while it meets no diffculty with anisotropy data at angular scales $\gamma < 1^\circ$, is usefully constrained by data at $1^\circ < \gamma < 90^\circ$. We impose limits on the rms perturbation amplitude at thermal decoupling, which depend on $\gamma^*$, the angular size of the fractal cell. A recently claimed detection of anisotropy at the scale of $8^\circ$ is also discussed in the light of the model.

The definition of the correlation function is not unique and depends on thefreedom in choosing the normalization constraint. Such a lackness of uniqueness strongly influences the correlation amplitude and, as a consequence, may change the interpretation of physical quantities in the system considered.This effect occurs in systems where it is not possible to define a mean value for the probability distribution of the average densities (e.g., an infinite fractal), while in the opposite case (as, for instance, liquids, where the average density is well defined, since it does not depend on the sample geometry) there is no contradiction between the different definitions of the correlation function. In this paper we indicate the sample dependence of the amplitudes of the different correlation functions in sets where the mean density of the statistical population is unknown or cannot be defined.

The two-point angular correlation function of galaxies is determined as a function of magnitude limit (i.e. depth) for the sample of galaxies in the Zwicky catalogue. The observed scaling of the correlation function with depth is compared with that expected from the following models: the standard clustering model within a generally homogeneous medium; a pure fractal model; and a cell-fractal model. We find that a pure fractal model is inconsistent with the data, in accord with previous observations. The homogeneous model and a cell-fractal model with an upper cut-off radius $R_co\sim 30 h^-1$ Mpc are both consistent with the present data.

We presented explicit forms of 2-- and 3--point spatial correlation function for observer homogeneous and slf--similar structure. Our results have a little difference with the usual form in the 3--point case, but it is the same in the sense of the second order of the 2--point function.

Constraints on chemical potentials and masses of "inos'' are calculated using cosmological standard nucleosynthesis processes. It is shown that the electron neutrino chemical potential, $\xi_\nu_e$, should not be greater than a value of order of 1 and the possible effective chemical potential of the other neutrino species, $\xi$, and electron neutrino chemical potential are related approximately $10\xi_\nu_e \sim \xi$ in order not to conflict with observational data. The allowed regions consistent with the $^4$He abundance observations are insensitive to the baryon--to--proton ratio, $\eta$, while those imposed by other light elements (D, $^3$He, $^7$Li) strongly depend on $\eta$. Values of the chemical potentials calculated by Ruffini etal., in a previous paper in the series, on the basis of a cellular large--scale structure of the universe are shown to be consistent with cosmological nucleosynthesis.

Constraints on chemical potentials and masses of "inos'' are calculated using cosmological standard nucleosynthesis processes. It is shown that the electron neutrino chemical potential, $\xi_\nu_e$, should not be greater than a value of order of 1 and the possible effective chemical potential of the other neutrino species, $\xi$, and electron neutrino chemical potential are related approximately $10\xi_\nu_e \sim \xi$ in order not to conflict with observational data. The allowed regions consistent with the $^4$He abundance observations are insensitive to the baryon--to--proton ratio, $\eta$, while those imposed by other light elements (D, $^3$He, $^7$Li) strongly depend on $\eta$. Values of the chemical potentials calculated by Ruffini etal., in a previous paper in the series, on the basis of a cellular large--scale structure of the universe are shown to be consistent with cosmological nucleosynthesis.

We realize the description of the cellular structure of the universe with a power law distribution of matter within the framework of generalized Friedmann model. The inhomogeneity is normalized to present matter distribution. The distortion in Hubble flow by density inhomogeneity is calculated for different models. The extrapolation procedure for a global Hubble constant and other cosmological quantities are discussed. It is shown that the distortion in the Hubble flow has great meaning in the common cosmological tests as well as in the measurement of density distribution, clustering properties and peculiar velocities on large scales.

Density fluctuations of a cosmological quantum real scalar field in a coherent state are interpreted as Bogoliubov compressional excitations of a condensed Bose--Einstein gas. The Jeans instability mechanism is generalized in this funy quantum context. The evolution of the Jeans mass in a FRW Universe that emerges from an inflationary stage is then studied in the nonrelativistic and ultrarelativistic phases. The behavior of the Jeans mass is found to be qualitatively similar, although quantitatively different, to that of a fermion matter field. The introduction of the gauge--invariant formalism is necessary to find the time evolution of the perturbations in the radiation dominated stage.

Selfgravitating systems of classical particles with two distribution functions with different law of cutoff are considered: one corresponding to a truncated and one to a smoothed distribution. The results are compared and contrasted and large differences are found for low values of a suitably defined cutoff parameter. Some well known results due to Zel'dovich and Podurets are shown to be a consequence only of an arbitrary constraint imposed, by them, on the entire family of solutions.

The semidegenerate equilibrium configurations of a selfgravitating system of fermions have usually been treated by an expansion of the thermodynamical quantities around the fully degenerate values. It is shown that such an expansion is invalid in the low density regimes where in general a distribution function far from the degenerate one applies. This point is explicitly illustrated by comparing and contrasting the results based on a first and second order expansionfrom the fully degenerate values with the exact ones. These exact values have been obtained by a direct computation of the Fermi integrals. We find that for any value of the temperature $T \neq 0$, a system selfgravitating fermions leads to a configuration of equilibrium with a density decreasing at large distances as $\rho \sim r^-2$, quite independantly of the value of its central density, and, therefore, always infinite both in mass and radius.

We examine the Newtonian equilibrium configurations of a system of bosons undergoing quantum condensation, with a distribution function with a cut--off in the momentum space. Bounded configurations with a core of condensed particles surrounded by an uncondensed phase are obtained. The results are compared and contrasted with the ones in which the spatial divergences are removed by a cut--off in density. The well--known solution corresponding to fully condensed configurations is obtained for suitable values of the central density.

Generalization of the velocity field in an anisotropic and inhomogeneous ellipsoid to the non linear case proposed in a previous paper is extended to cover the most general directions of the vorticity and angular velocity. A Roberts form for density is used instead of the restricted Ferrers density. Equilibrium sequences are determined and their stability against odd and even modes of oscillation is discussed. Dedekind's and Riemann's theorems are extended. We also examine the dynamical case and the angular momentum, precession, vorticity and energy of the sequences.

In this paper we wish to follow the evolution of a selfgravitating axisymmetric mass rotating differentially around the axis of symmetry. We study the finite oscillation about the spheroidal form solving the Eulerian equations. Also the stability of these dynamical solutions is discussed. This problem can be applied to follow the secular evolution of the velocity field and distribution of matter of a high angular momentum star.

Based on Cahndrasekhar's and Lebovitz's treatment of the roto-vibrational modes of a homogeneous compressible star, the energy losses and damping rates of each mode by gravitational radiation are computed as a function of the eccentricity e of the equilibrium configuration. Numerical values are estimated for a neutron star. The limit of low eccentricity is considered, compared and contrasted to exixting treatment.

We defined a directional two points correlation function to analyze the rich structures of the universe. Here we discussed the definition of this function and the possible estimators for this fiunction. This directional correlation function strongly dependes on the distribution property of the universe, say string, sheet and sphere like clustering. Hence this function can be used to measure various structures of galaxy distribution for various scales.

We present explicit forms of two and three points spatial correlation functions for observer homogeneous and self similar structure. We obtained the two points one with the same form of Calzetti, et al., 1988, that is, power law with the sample size dependent amplitude. But three points one has the linear terms of the two points one, which was ignored in the usual hierarchical form, with overall coefficient 1/3, which is expected to be 1 in the usual hierarchical form. The crucial difference of our theoretical form is that it is increasing function of separation after a certain scale. Of course, our theoretical form does not contain any observational effects, say selection function, thus our results can not be compared directly with the real catalogue data unless we use a correct estimator for correlation functions. Assuming the selection effect is only given by the Schechter luminosity function and using the estimator expected by the theoretical derivation, we measured the two and three points functions for CfA catalogue. Our results for two points function gives the rather small power index, approximately 1.1. and shows the power law feature continue only up the scale 25 Mpc.

We provide detailed calculations of the anisootropies of the microwave background from the arcminute range to the quadrupole scale, for the cellular-fractal universe introduced in Paper I of this series. Contrary to earlier estimates, we find that the model is consistent with microwave data for a fractal cell radius $R<50 h^-1 Mpc$. The resulting picture also agrees with very recent astronomical observations, including the striking results of Broadhurst et al. (1990), which constitute a hard challenge for standard power-law theories of galaxy formation. We show that the anisotropies in the background radiation should be looked for mainly in the arcminute range, a direct imprint of the cosmic cell radius being predicted around 10'-20'.

We study the gravitational equilibrium of static, spherically symmetric, Newtonian systems consisting of a collisionless semidegenerate Fermi gas. A cutoff in the phase space distribution function of the particles is introduced in order to avoid the problems arising from the infinite radius of semidegenerate configurations when the usual Fermi-Dirac function is used. We consider, here, the more general case of a cutoff in energy and angular momentum, the latter giving an anisotropy in the velocity space. The treatment is applied to model massive galactic halos. Limits on the mass of the "inos" composing the halos are derived both from phase space constraints and from general features of the observed rotation curves in spiral galaxies.

The problem of the gravithermal instability is studied in the case of N-body selfgravitating systems with a King-like distribution function. Introducing a suitable \it effective potential the distribution is led to the Boltzmann one. At any radius $r$ the system looks like an ideal gas submitted to an "external field". Due to the presence of the cut-off, a different behaviour is found with respect to the classical Lynden-Bell and Wood treatment.

We study the gravitational equilibrium of systems composed byfermions obeying a modified Fermi-Dirac distribution function. An energy cutoff in the phase space is introduced to account for the existence of an escape velocity from the system. We further consider an angular momentum cutoff giving an anisotropy in the velocity space. Limits on the fermion mass are derived both from phase space constraints and from general features of the observed rotation curves in spiral galaxies.

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered. The method considers a simple non-Maxwellian distribution function, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant during collisionless perturbations: $f_a\sim\exp\-[p^2c^2(R/R_0)^2+m^2c^4]^1/2/kT\$. The method considered here gives approximate results about the stability, because adiabatic perturbations of Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analytically. Nevertheless the results are much closer to the results of numerical simulations than the original ZP ones.

The problem of the gravithermal instability is studied in the case of N-body selfgravitating systems with a King-like distribution function. Introducing a suitable \it effective potential the distribution is led to the Boltzmann one. At any radius $r$ the system looks like an ideal gas submitted to an "external field". Due to the presence of the cut-off, a different behavior is found with respect to the classical Lynden-Bell and Wood treatment.

The semidegenerate equilibrium configurations of a selfgravitating system of fermions have usually been treated by an expansion of the thermodynamical quantities around the fully degenerate values. It is shown that such an expansion is invalid in the low density regimes where in general a distribution function far from the degenerate one applies. This point is explicitly illustrated by comparing and contrasting the results based on a first and second order expansion from the fully degenerate values with the \it exact ones. These exact values have been obtained by a direct computation of the Fermi integrals. We find that for \it any value of the temperature $T\neq 0$, a system of selfgravitating fermions leads to a configuration of equilibrium with a density decreasing at large distances as $\rho\sim r^-2$, quite independently on the value of its central density, and, therefore, \it always infinite both in mass and radius.

In this paper, we start to investigate on a class of solutions of Jeans equations for axisymmetric models of elliptical galaxies, characterized by a low rotation velocity and a relatively high dispersion velocity, as seems to be the case for "real" ellipticals. Nevertheless, we want to stress that it is possible to construct these models starting from a distribution function that depends only on two classical integrals of motion, the energy and the component of angular momentum along the symmetry axis and therefore without " radial" anisotropy in the dispersion velocity tensor.

The time-scales corresponding to the violent relaxation phase, to the subsequent collective relaxation phase and to the final binary relaxation phase are treated in the framework of the theory of flows in configuration manifolds of negative curvature. An unified picture of relaxation processes in stellar dynamics is therefore obtained.

A rigorous treatment of the violent relaxation phase of a large self-gravitating stellar system is made in the framework of the analytical dynamics. In the regime in which the coarse-grained virial theorem can be applied, the stellar system can be considered a \it mixing system. The consequent instability of the Anossov flow leads to the evaluation of the violent relaxation time scale.

We examine self-gravitating systems made of a mixture of condensed bosons and degenerate fermions in the Newtonian regime. We develop a numerical approach to determine the relevant quantities of the equilibrium configurations. An analytical treatment is also obtained in the limits in which the central density of one component is dominant. For the case in which the fermions are neutrons and the boson mass in greater than $10^-7eV c^-2$ , we find : 1) for those configurations in which the central density of fermions dominates, the gravitational field confines the boson component to a region smaller than that occupied by the corresponding pure boson configuration. The size of such region $R_B \sim (\hbar/m_B \sqrtG \rho_F(0))^1/2$ is independent of the boson number and relates to the fermion density; 2) both in the cases of a boson density smaller or larger than the fermion density, the bosons do not perturb significantly the fermions, which distribute according to the usual solution of Chandrasekhar.

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered.

A new thermodynamic treatment of selfgravitating systems is given in the "mean field approximation". The introduction of a suitable \it effective potential let a King-like distribution function to be led to a Boltzmann one. In this context, the stability of the equilibrium configurations is investigated under small departures from thermal equilibrium.

Stability of dense stellar clusters to relativistic collapse is investigated by approximate methods, similar to the static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich \& Podurets (ZP), have been considered. The first method is based on the choice of the sequence of Maxwellian models with fixed cutoff parameter, in accordance with adiabatic conditions $p_cut\sim n_c^1/3$. The second one is based on the consideration of the sequence of Maxwellian models with the same value of the total entropy $S=\int\!\!\!\int f(1-\ln f)d\vec pd\vec r$. The third method considers simple non-Maxwellian distribution function of the clusters, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant: $f\sim\exp\-[p^2c^2(n_c0/n_c)^2/3+m^2c^4]^1/2/T\$. The methods considered here give approximate results about the stability, because adiabatic perturbations of Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analitically. Nevertheless these results are better than ones obtained from the considerations of the sequence of Maxwellian models with different temperature, made by ZP. They are more close to the results of numerical simulation than original ZP ones. The coincidence of the temperatures in the critical point, $T=0.223~mc^2$, obtained by two last methods, makes us to believe that these methods, being approximate, give rather good relative precision, which is not worse than $10^-3$.

The present status of the analysis of relaxation to equilibrium in \it N-body self-gravitating systems is blocked on the (unsolved) juxtaposition between the results of the classical theory of the binary relaxation (Chandrasekhar, 1942; Binney \& Tremaine, 1987) and that based on the ergodic theory of dynamical systems (Gurzadyan \& Savvidy, 1986 (GS); Kandrup, 1989).

We present a possible explanation of the different mechanism involved in the two kinds of relaxation and discuss some consequences, physical as astronomical, thereof.

In this paper we use the results of a previous work to show an alternative explanation to the problem of slowly rotating elliptical galaxies. The main issue of our analysis is that it is possible to construct fully analytical solution of Jeans equations, with rotation and dispersion velocity curves in agreement with observational results, \it and that this can be achieved even when the distribution function $f(\xx,\vv)$ depends only on two isolating integrals of motion.

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered. The method considers a simple non-Maxwellian distribution function, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant during non collisional perturbations: $f_a\sim\exp\p^2c^2(R/R_0)^2+m^2c^4]^1/2/kT\$. The method considered here gives results coincident with the ones carried out by the method based on sequences at constant entropy. These results are better than ones obtained from considerations of the sequence of Maxwellian models with different temperature, made by ZP. In particular they are much closer to the results of the numerical simulations of Shapiro and Teukolsky.

We provided detailed calculations of the anisotropies of the microwavebackground, from the arcminute range to the quadrupole scale, for thecellular-fractal universe introduced in Paper I of this series. Contrary toearlier estimates, we find that the model is consistent with microwave data fora fractal cell radius $R,50h^{-1}$ Mpc. The resulting picture also agrees withvery recent astronomical observations including the striking results ofBroadhurst et. al.(1990) which constitute a hard challenge for standardpower-law theories of galaxy formation. We sho that the anisotripies in thebackground radiation should be looked for mainly in the arcminute range, adirect imprint of the cosmic cell radius being predicted around 10'-20'.\vfill\eject{\bf E - Sistemi Classici Autogravitanti}\pto{\bf E - Classical Selfgravitating Systems}\pto\

We study the gravitational equilibrium of static, spherically symmetric, Newtonian systems consisting of a collisionless semidegenerate Fermi gas. A cutoff in the phase space distribution function of the particles is introduced in order to avoid the problems arising from the infinite radius of semidegenerate configurations when the usual Fermi-Dirac function is used. We consider, here, the more general case of a cutoff in energy and angular momentum, the latter giving an anisotropy in the velocity space. The treatment is applied to model massive galactic halos. Limits on the mass of the "inos" composing the halos are derived both from phase space constraints and from general features of the observed rotation curves in spiral galaxies. \pto\

We study the gravitational equilibrium of systems composed byfermions obeying a modified Fermi-Dirac distribution function. An energy cutoff in the phase space is introduced to account for the existence of an escape velocity from the system. We further consider an angular momentum cutoff giving an anisotropy in the velocity space. Limits on the fermionmass are derived both from phase space constraints and from general features of the observed rotation curves in spiral galaxies. \pto\

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered. The method considers asimple non-Maxwellian distribution function, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant during collisionless perturbations: $f_a\sim\exp\{-[p^2c^2(R/R_0)^2+m^2c^4]^{1/2}/kT\}$. The method considered here gives approximate results about the stability, because adiabatic perturbations of Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analytically. Nevertheless the resultsare much closer to the results of numerical simulations than the original ZP ones. \pto\

The problem of the gravithermal instability is studied in the case of N-body selfgravitating systems with a King-like distribution function. Introducing a suitable {\it effective potential} the distribution is led to the Boltzmann one. At any radius $r$ the system looks like an ideal gas submitted to an "external field". Due to the presence of the cut-off, a different behavior is found with respect to the classical Lynden-Bell and Wood treatment. \pto\

In this paper, we start to investigate on a class of solutions of Jeans equations for axisymmetric models of elliptical galaxies, characterizedby a low rotation velocity and a relatively high velocity dispersion, as seems to be the case for {\sl "real"} ellipticals.\ Nevertheless, we want to stress that it is possible to construct these models starting from a distribution function that depends only on two classical integrals of motion, the energy and the component of angular momentum along the symmetry axis, and therefore without{\it "radial"} anisotropy in the velocity dispersion tensor.\

The present status of the analysis of relaxation to equilibrium in {\it N-bodyself-gravitating systems} is blocked on the (unsolved) juxtaposition betweenthe results of the classical theory of the binary relaxation (Chandrasekhar,1942; Binney \& Tremaine, 1987) and that based on the ergodic theory ofdynamical systems (Gurzadyan \& Savvidy, 1986 (GS); Kandrup, 1989).We present a possible explanation of the different mechanism involved in the two kinds of relaxation and discuss some consequences, physical as astronomical, thereof.\

We defined a directional two points correlation function to analyze the structure of the universe. We analyze CfA catalogue using this directional two points correlation function instead of usual correlation function. This directional correlation function strongly depend on the distribution property of the universe, say string, sheet and sphere like clustering. This analysis will give a clue to distinguish between small and large scale clustering properties. \

The problem of the gravithermal instability is studied in the case of N-body selfgravitating systems with a King-like distribution function. Introducing a suitable {\it effective potential} the distribution is led to the Boltzmann one. At any radius $r$ the system looks like an ideal gas submitted to an "external field". Due to the presence of the cut-off, a different behaviour is found with respect to the classical Lynden-Bell and Wood treatment. \pto\

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered. \pto\

Stability of dense stellar clusters to relativistic collapse is investigated by an approximate method, similar to static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich and Podurets (ZP), have been considered. The method considers asimple non-Maxwellian distribution function, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant during non collisionalperturbations: $f_a\sim\exp\{-[p^2c^2(R/R_0)^2+m^2c^4]^{1/2}/kT\}$. The methodconsidered here gives results coincident with the ones carried out by the method based on sequences at constant entropy. These results are better than ones obtained from considerations of the sequence of Maxwellian models with different temperature, made by ZP. In particular they are much closer to the results of the numerical simulations of Shapiro and Teukolsky. \pto\

A new thermodynamic treatment of selfgravitating systems is given in the "mean field approximation". The introduction of a suitable {\it effective potential} let a King-like distribution function to be led to a Boltzmann one. In this context, the stability of the equilibrium configurations is investigated under small departures from thermal equilibrium. \pto\

Stability of dense stellar clusters to relativistic collapseis investigated by approximate methods, similar to the static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich \& Podurets (ZP), have been considered. Thefirst method is based on the choice of the sequence of Maxwellian models with fixed cutoff parameter, in accordance with adiabatic conditions $p_{cut}\sim n_c^{1/3}$. The second one is based on the consideration of the sequence of Maxwellian models with the same value of the total entropy $S=\int\!\!\!\int f(1-\ln f)d{\vec p}d{\vec r}$. The third method considerssimple non-Maxwellian distribution function of the clusters, obtained from the Maxwellian one by the condition of conservation of adiabatic invariant: $f\sim\exp\{-[p^2c^2(n_{c0}/n_c)^{2/3}+m^2c^4]^{1/2}/T\}$. The methods considered here give approximate results about the stability, because adiabatic perturbations of Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analitically. Nevertheless these results are better than ones obtained from the considerations of the sequence of Maxwellian models with different temperature, made by ZP. They are more close to the results of numerical simulation than original ZP ones. The coincidence of the temperatures in the critical point, $T=0.223~mc^2$, obtained by two last methods, makes us to believe that these methods, being approximate, give rather good relative precision, which is not worse than $10^{-3}$. \pto\

In this paper we use the results of a previous work to show an alternative explanation to the problem of slowly rotating ellipticalgalaxies. The main issue of our analysis is that it is possible to constructfully analytical solution of Jeans equations, with rotation and dispersionvelocity curves in agreement with observational results, {\it and} thatthis can be achieved even when the distribution function $f(\xx,\vv)$ dependsonly on two isolating integrals of motion.}\

Application of non-Riemannian geometries with an asymmetric metric tensor to the problem of geometric unification is discussed. An approach to a classification for such kind of geometries in spirit of Schouten is proposed.

The "dyadosphere" (from the Greek word "duas-duados" for pairs) is here defined as the region outside the horizon of a black hole endowed with an electromagnetic field (abbreviated to EMBH for "electromagnetic black hole") where the electromagnetic field exceeds the critical value, predicted by Heisenberg and Euler for electron-positron pair production.
In a very short time, a very large number of pairs is created there. I give limits on the EMBH parameters leading to a Dyadosphere for 10 solar mass and 100000 solar mass EMBH's, and give as well the pair densities as functions of the radial coordinate. These data give the initial conditions for the analysis of an enormous pair-electromagnetic-pulse or "PEM-pulse" which naturally leads to relativistic expansion. Basic energy requirements for gamma ray bursts (GRB), including GRB971214 recently observed at z=3.4, can be accounted for by processes occurring in the dyadosphere.

Recent works on the Dyadosphere are reviewed

Recent works on the Dyadosphere are reviewed

Using hydrodynamic computer codes, we study the possible patterns of relativistic expansion of an enormous pair-electromagnetic-pulse (P.E.M. pulse); a hot, high density plasma composed of photons, electron-positron pairs and baryons deposited near a charged black hole (EMBH). On the bases of baryon-loading and energy conservation, we study the bulk Lorentz factor of expansion of the P.E.M. pulse by both numerical and analytical methods.

On the non-riemannian manifolds as framework for geometric unification theories affine connection geometry with asymmatric metric Recent Developments in Theoretical and Experimental General Relativity, Gravitation and relativistic field theories, held at the Hebrew University in Jerusalem, 22-27 june 1997. Edited by Tsvi Piran and Remo Ruffini. World Scientific Publishers, 1999, p. 436.

 R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, S.-S. Xue, On the interpretation of the burst structure of GRBs, Ap.J. 555 (2001), L113

Given the very accurate data from the BATSE experiment and RXTE and Chandra satellites, we use the GRB 991216 as a prototypical case to test the EMBH theory linking the origin of the energy of GRBs to the electromagnetic energy of black holes. The fit of the afterglow fixes the only two free parameters of the model and leads to a new paradigm for the interpretation of the burst structure, the IBS paradigm. It leads as well to a reconsideration of the relative roles of the afterglow and burst in GRBs by defining two new phases in this complex phenomenon: a) the injector phase, giving rise to the proper-GRB (P-GRB), and b) the beam-target phase, giving rise to the extended afterglow peak emission (E-APE) and to the afterglow. Such differentiation leads to a natural possible explanation of the bimodal distribution of GRBs observed by BATSE. The agreement with the observational data in regions extending from the horizon of the EMBH all the way out to the distant observer confirms the uniqueness of the model.

Giuliano Preparata Remo Ruffini, She-Sheng Xue, The role of the screen factor in GRBs, IL Nuovo Cimento Vol. 115 B N.7-9 (2000) 915

We derive the screen factor for the radiation flux from an optically thick plasma of electron-positron pairs and photons, created by vacuum polarization process around a black hole endowed with electromagnetic structure.

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, S.-S. Xue, On the physical processes which lie at the bases of time variability of GRBs, Il Nuovo Cimento Vol. 116 B, n. 1, 99 (2001)

The relative-space-time-transformation (RSTT) paradigm and the interpretation of the burst-structure (IBS) paradigm are applied to probe the origin of the time variability of GRBs. Again GRB 991216 is used as a prototypical case, thanks to the precise data from the CGRO, RXTE and Chandra satellites. It is found that with the exception of the relatively inconspicuous but scientifically very important signal originating from the initial "proper gamma ray burst'' (P-GRB), all the other spikes and time variabilities can be explained by the interaction of the accelerated-baryonic-matter pulse with inhomogeneities in the interstellar matter. This can be demonstrated by using the RSTT paradigm as well as the IBS paradigm, to trace a typical spike observed in arrival time back to the corresponding one in the laboratory time. Using these paradigms, the identification of the physical nature of the time variablity of the GRBs can be made most convincingly. It is made explicit the dependence of a) the intensities of the afterglow, b) the spikes amplitude and c) the actual time structure on the Lorentz gamma factor of the accelerated-baryonic-matter pulse. In principle it is possible to read off from the spike structure the detailed density contrast of the interstellar medium in the host galaxy, even at very high redshift.

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, S.-S. Xue, On a possible GRB-supernova time sequence, AASTeX, 7 pages, 2 figures,  Ap.J. 555 (2001), L117

The data from the Chandra satellite on the iron emission lines in the afterglow of GRB 991216 are used to give further support for the EMBH theory, which links the origin of the energy of GRBs to the extractable energy of electromagnetic black holes (EMBHs), leading to an interpretation of the GRB-supernova correlation. Following the relative space-time transformation (RSTT) paradigm and the interpretation of the burst structure (IBS) paradigm, we introduce a paradigm for the correlation between GRBs and supernovae. The following sequence of events is shown as kinematically possible and consistent with the available data: a) the GRB-progenitor star $P_1$ first collapses to an EMBH, b) the proper GRB (P-GRB) and the peak of the afterglow (E-APE) propagate in interstellar space until the impact on a supernova-progenitor star $P_2$ at a distance $\le 2.69\times 10^{17}$ cm, and they induce the supernova explosion, c) the accelerated baryonic matter (ABM) pulse, originating the afterglow, reaches the supernova remnants 18.5 hours after the supernova explosion and gives rise to the iron emission lines. Some considerations on the dynamical implementation of the paradigm are presented. The concept of induced supernova explosion introduced here specifically for the GRB-supernova correlation may have more general application in relativistic astrophysics.

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, S.-S. Xue, Relative space-time transformations in GRBs, AASTeX, 10 pages, 2 figures,  Ap.J. 555 (2001), L107

The GRB 991216 and its relevant data acquired from the BATSE experiment and RXTE and Chandra satellites are used as a prototypical case to test the theory linking the origin of gamma ray bursts (GRBs) to the process of vacuum polarization occurring during the formation phase of a black hole endowed with electromagnetic structure (EMBH). The relative space-time transformation paradigm (RSTT paradigm) is presented. It relates the observed signals of GRBs to their past light cones, defining the events on the worldline of the source essential for the interpretation of the data. Since GRBs present regimes with unprecedently large Lorentz $\gamma$ factor, also sharply varying with time, particular attention is given to the constitutive equations relating the four time variables: the comoving time, the laboratory time, the arrival time at the detector, duly corrected by the cosmological effects. This paradigm is at the very foundation of any possible interpretation of the data of GRBs.

294

Remo J. Ruffini, Analogies, new paradigms and observational data as growing factors of Relativistic Astrophysics, 28 pages, 14 figures, to appear in "Fluctuating Paths and Fields - Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday", Eds. W. Janke, A. Pelster, H.-J. Schmidt, and M. Bachmann (World Scientific, Singapore, 2001), p. 771

Patterns in the scientific developments of Relativistic Astrophysics are analyzed with special attention to the physics and astrophysics of Black Holes and Gamma Ray Bursts.

295

G.Bertone, R.Ruffini,  Relativistic Thomas-Fermi Model at Finite Temperatures, 8 pages, Latex wsp9.cls. Proceedings Marcel Grossmann IX, Rome (Italy), 2-9 July 2000 (World Scientific)

We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite temperatures in the non-relativistic approximation and present a new relativistic model at finite temperatures, investigating how to recover the existing theory in the limit of low temperatures. This work is intended to be a propedeutical study for the evaluation of equilibrium configurations of relativistic "hot'' white dwarfs.

296 

Carlo Luciano Bianco, Remo Ruffini, She-Sheng Xue, The elementary spike produced by a pure $e^+e^-$ pair-electromagnetic pulse from a Black Hole: The PEM Pulse, 14 pages, 18 figures, to appear in Astronomy & Astrophysics Journal-ref: Astron.Astrophys. 368 (2001) 377-390

In the framework of the model that uses black holes endowed with electromagnetic structure (EMBH) as the energy source, we study how an elementary spike appears to the detectors. We consider the simplest possible case of a pulse produced by a pure $e^+e^-$ pair-electro-magnetic plasma, the PEM pulse, in the absence of any baryonic matter. The resulting time profiles show a {\em Fast-Rise-Exponential-Decay} shape, followed by a power-law tail. This is obtained without any special fitting procedure, but only by fixing the energetics of the process taking place in a given EMBH of selected mass, varying in the range from 10 to $10^3$ $M_\odot$ and considering the relativistic effects to be expected in an electron-positron plasma gradually reaching transparency. Special attention is given to the contributions from all regimes with Lorentz $\gamma$ factor varying from $\gamma=1$ to $\gamma=10^4$ in a few hundreds of the PEM pulse travel time. Although the main goal of this paper is to obtain the elementary spike intensity as a function of the arrival time, and its observed duration, some qualitative considerations are also presented regarding the expected spectrum and on its departure from the thermal one. The results of this paper will be comparable, when data will become available, with a subfamily of particularly short GRBs not followed by any afterglow. They can also be propedeutical to the study of longer bursts in presence of baryonic matter currently observed in GRBs.

297

Costantino Sigismondi, Simonetta Filippi, Luis Alberto Sanchez, Remo Ruffini, Damping time and stability of density fermion perturbations in the expanding universe, 14 pages, 4 figures, submitted to IJMP-D

The classic problem of the growth of density perturbations in an expanding Newtonian universe is revisited following the work of Bisnovatyi-Kogan and Zel'dovich. We propose a more general analytical approach: a system of free particles satisfying semi-degenerate Fermi-Dirac statistics on the background of an exact expanding solution is examined in the linear approximation. This differs from the corresponding work of Bisnovatyi-Kogan and Zel'dovich where classical particles fulfilling Maxwell-Boltzmann statistics were considered. The solutions of the Boltzmann equation are obtained by the method of characteristics. An expression for the damping time of a decaying solution is discussed and a zone in which free streaming is hampered is found, corresponding to wavelengths less than the Jeans one. In the evolution of the system, due to the decrease of the Jeans length, those perturbations may lead to gravitational collapse. At variance with current opinions, we deduce that perturbations with lambda >=lambda_(J Max)/1.48 are able to generate structures and the lower limit for substructures mass is M = M_(J max)/(1.48)^3 ~ M_(J max)/3, where M_(J max) is the maximum value of the Jeans mass.

298

Remo J. Ruffini, Black holes and gamma ray bursts: background for the theoretical model, 33 pages, 19 figures, to appear in the "Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity (MGIXMM)", World Scientific (Singapore, in press)

The idea that the vacuum polarization process occurring during gravitational collapse to a black hole endowed with electromagnetic structure (EMBH) could be the origin of gamma ray bursts (GRBs) is further developed. EMBHs in the range 3.2 -- 10$^6$ solar masses are considered. The formation of such an EMBH, the extraction of its mass-energy by reversible transformations and the expansion of the pair-electromagnetic pulse (PEM pulse) are all examined within general relativity. The PEM pulse is shown to accelerate particles to speeds with Lorentz gamma factors way beyond any existing experiment on Earth. Details of the expected burst structures and other observable properties are examined.

299

Remo Ruffini, Luca Vitagliano, Irreducible mass and energetics of an electromagnetic black hole, 8 pages, 1 figure, to appear on Physics Letters B, Phys.Lett. B545 (2002) 233-237

The mass-energy formula for a black hole endowed with electromagnetic structure (EMBH) is clarified for the nonrotating case. The irreducible mass $M_{\mathrm{irr}}$ is found to be independent of the electromagnetic field and explicitly expressable as a function of the rest mass, the gravitational energy and the kinetic energy of the collapsing matter at the horizon. The electromagnetic energy is distributed throughout the entire region extending from the horizon of the EMBH to infinity. We discuss two conceptually different mechanisms of energy extraction occurring respectively in an EMBH with electromagnetic fields smaller and larger than the critical field for vacuum polarization. For a subcritical EMBH the energy extraction mechanism involves a sequence of discrete elementary processes implying the decay of a particle into two oppositely charged particles. For a supercritical EMBH an alternative mechanism is at work involving an electron-positron plasma created by vacuum polarization. The energetics of these mechanisms as well as the definition of the spatial regions in which thay can occur are given. The physical implementations of these ideas are outlined for ultrahigh energy cosmic rays UHECR) and gamma ray bursts (GRBs).

300

Christian Cherubini, Remo Ruffini, Luca Vitagliano, On the electromagnetic field of a charged collapsing spherical shell in general relativity,  8 pages, 2 figures, to appear on Physics Letters B,  Phys.Lett. B545 (2002) 226-232

A new exact solution of the Einstein-Maxwell equations for the gravitational collapse of a shell of matter in an already formed black hole is given. Both the shell and the black hole are endowed with electromagnetic structure and are assumed spherically symmetric. Implications for current research are outlined.

301

Giuliano Preparata, Remo Ruffini, She-Sheng Xue, On the Dyadosphere of Black Hole, 10 pages, 4 figures

Basic energy requirements of Gamma Ray Burst(GRB) sources can be easily accounted for by a pair creation process occurring in the "Dyadosphere" of a Black Hole endowed with an electromagnetic field (abbreviated to EMBH for "electromagnetic Black Hole"). This includes the recent observations of GRB971214 by Kulkarni et al. The "Dyadosphere" is defined as the region outside the horizon of an EMBH where the electromagnetic field exceeds the critical value for e^+ e^- pair production. In a very short time $\sim O(hbar mc^2}), very large numbers of pairs are created there. Further evolution then leads naturally to a relativistically expanding pair-electromagnetic-pulse (PEM-pulse). Specific examples of Dyadosphere parameters are given for 10 and 10^5 solar mass EMBH's. This process does occur for EMBH with charge-to-mass ratio larger than 2.210^{-5} and strictly smaller than one. From a fundamental point of view, this process represents the first mechanism proved capable of extracting large amounts of energy from a Black Hole with an extremely high efficiency (close to 100%).

301

Remo J. Ruffini, Gamma Ray Bursts and vacuum polarization process in electromagnetic Black Holes,  23 pages, 11 figures, in the proceeding of the conference "18th Advanced Icfa Beam Dynamics Workshop On Quantum Aspects Of Beam Physics" edited by P.C. Chen, Capri, October 15-20, 2000, World Scientific, Singapore, 2001

The developments of the elctromgnetic black holes physics and vacuum polarization process are presented in the interpretation of Gamma-Ray Bursts.

302

Remo Ruffini, Observational tests of the Electro-Magnetic Black Hole Theory in Gamma-Ray Bursts, 19 pages, 11 figures, in Proceedings of the meeting "Lighthouses in the Universe", Springer-Verlag, Berlin, 2002

The Relative Space-Time Transformation (RSTT) Paradigm and the Interpretation of the Burst Structure (IBS) Paradigm are applied to the analysis of the structure of the burst and afterglow of Gamma-Ray Bursts within the theory based on the vacuum polarization process occurring in an Electro-Magnetic Black Hole, the EMBH theory. This framework is applied to the study of the GRB991216 which is used as a prototype. The GRB-Supernova Time Sequence (GSTS) Paradigm, which introduces the concept of induced gravitational collapse in the Supernovae-GRB association, is announced and will be applied, within the EMBH theory, to GRB980425 as a prototype in a forthcoming paper.

303

Using GRB 991216 as a prototype, it is shown that the intensity substructures observed in what is generally called the "prompt emission" in gamma ray bursts (GRBs) do originate in the collision between the accelerated baryonic matter (ABM) pulse with inhomogeneities in the interstellar medium (ISM). The initial phase of such process occurs at a Lorentz factor $\gamma\sim 310$. The crossing of ISM inhomogeneities of sizes $\Delta R\sim 10^{15}$ cm occurs in a detector arrival time interval of $\sim 0.4$ s implying an apparent superluminal behavior of $\sim 10^5c$. The long lasting debate between the validity of the external shock model vs. the internal shock model for GRBs is solved in favor of the first.

304

Ruffini R., Bianco C.L., Chardonnet P., Fraschetti F., Xue S.S., “On the structures in the Afterglow Peak Emission of Gamma-Ray Bursts”, ApJ, 581, L19, 2002

Using GRB~991216 as a prototype, it is shown that the intensity substructures observed in what is generally called the "prompt emission'' in gamma ray bursts (GRBs) do originate in the collision between the accelerated baryonic matter pulse with inhomogeneities in the interstellar medium (ISM). The initial phase of such process occurs at a Lorentz factor $\gamma\sim 310$. The crossing of ISM inhomogeneities of sizes $\Delta R\sim 10^{15}\, {\rm cm}$ occurs in a detector arrival time interval of $\sim 0.4\, {\rm s}$ implying an apparent superluminal behavior of $\sim 10^5c$. The long lasting debate between the validity of the external shock model versus the internal shock model for GRBs is solved in favor of the first.

305

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, S.-S. Xue; "The EMBH model in GRB 980425 and GRB 991216"; Proceedings of "Gamma-ray bursts in the Afterglow Era, 3rd workshop" in Rome (2002)

This is a summary of the talks presented at the Rome GRB meeting by C.L. Bianco and R. Ruffini. It was shown that by respecting the relative space-time transformation paradigm (RSTT), important inferences are possible in the new physics occurring in the energy sources of GRBs, on the structure of the bursts as well as on the composition of the interstellar matter surrounding the source. All current theoretical models of GRBs, by neglecting the implementation of this paradigm, lack the fundamental cognitive tools relating the physical nature of the source to the received GRBs light signals.

306

The idea that the vacuum polarization process occurring during gravitational collapse to a black hole endowed with electromagnetic structure (EMBH) could be the origin of gamma ray bursts (GRBs) is further developed. EMBHs in the range 3.2 -- 10$^6$ solar masses are considered. The formation of such an EMBH, the extraction of its mass-energy by reversible transformations and the expansion of the pair-electromagnetic pulse (PEM pulse) are all examined within general relativity.

The PEM pulse is shown to accelerate particles to speeds with Lorentz gamma factors way beyond any existing experiment on Earth.

Details of the expected burst structures and other observable properties are examined.

307

Remo Ruffini, Carlo Luciano Bianco and She-Sheng Xue, Pascal Chardonnet, Federico Fraschetti, World Scientic Publishing Company on the Structure of the Burst and Afterglow of  Gamma-Ray Bursts I: the Radial Approximation; International Journal of Modern Physics d; vol. 12, no. 2 (2003) 173-269

We have recently proposed three paradigms for the theoretical interpretation of gamma-ray bursts (GRBs). (1) The relative space-time transformation (RSTT) paradigm emphasizes how the knowledge of the entire world-line of the source from the moment of gravitational collapse is a necessary condition in order to interpret GRB data.\cite{lett1} (2) The interpretation of the burst structure (IBS) paradigm differentiates in all GRBs between an injector phase and a beam-target phase.\cite{lett2} (3) The GRB-supernova time sequence (GSTS) paradigm introduces the concept of {\em induced supernova explosion} in the supernovae-GRB association.\cite{lett3} The RSTT and IBS paradigms are enunciated and illustrated using our theory based on the vacuum polarization process occurring around an electromagnetic black hole (EMBH) theory. The results are summarized using figures, diagrams and a complete table with the space-time grid, the fundamental parameters and the corresponding values of the Lorentz gamma factor for GRB~991216 used as a prototype. In the following sections the detailed treatment of the EMBH theory needed to understand the results of the three above paradigms is presented. We start from the considerations on the dyadosphere formation. We then review the basic hydrodynamic and rate equations, the equations leading to the relative space-time transformations as well as the adopted numerical integration techniques. We then illustrate the five fundamental eras of the EMBH theory: the self acceleration of the $e^+e^-$ pair-electromagnetic plasma (PEM pulse), its interaction with the baryonic remnant of the progenitor star, the further self acceleration of the $e^+e^-$ pair-electromagnetic radiation and baryon plasma (PEMB pulse). We then study the approach of the PEMB pulse to transparency, the emission of the proper GRB (P-GRB) and its relation to the "short GRBs''. Particular attention is given to the free parameters of the theory and to the values of the thermodynamical quantities at transparency. Finally the three different regimes of the afterglow are described within the fully radiative and radial approximations: the ultrarelativistic, the relativistic and the nonrelativistic regimes. The best fit of the theory leads to an unequivocal identification of the "long GRBs'' as extended emission occurring at the afterglow peak (E-APE). The relative intensities, the time separation and the hardness ratio of the P-GRB and the E-APE are used as distinctive observational test of the EMBH theory and the excellent agreement between our theoretical predictions and the observations are documented. The afterglow power-law indexes in the EMBH theory are compared and contrasted with the ones in the literature, and no beaming process is found for GRB~991216. Finally, some preliminary results relating the observed time variability of the E-APE to the inhomogeneities in the interstellar medium are presented, as well as some general considerations on the EMBH formation. The issue of the GSTS paradigm will be the object of a forthcoming publication while the relevance of the iron-lines observed in GRB~991216 is shortly reviewed. The general conclusions are then presented based on the three fundamental parameters of the EMBH theory: the dyadosphere energy, the baryonic mass of the remnant, the interstellar medium density. An in depth discussion and comparison of the EMBH theory with alternative theories is presented as well as indications of further developments beyond the radial approximation, which will be the subject of paper II in this series.\cite{rbcfx02e_paperII} Future needs for specific GRB observations are outlined.

If due attention is given in formulating the basic equations for the Gamma-Ray Burst (GRB) phenomenon and in performing the corresponding quantitative analysis, GRBs open a main avenue of inquiring on totally new physical and astrophysical regimes. This program is very likely one of the greatest computational efforts in physics and astrophysics and cannot be actuated using shortcuts. A systematic approach is needed which has been highlighted in three basic new paradigms: the relative space-time transformation (RSTT) paradigm (\textcite{lett1}), the interpretation of the burst structure (IBS) paradigm (\textcite{lett2}), the GRB-supernova time sequence (GSTS) paradigm (\textcite{lett3}). From the point of view of fundamental physics new regimes are explored: (1) the process of energy extraction from black holes; (2) the quantum and general relativistic effects of matter-antimatter creation near the black hole horizon; (3) the physics of ultrarelativisitc shock waves with Lorentz gamma factor $\gamma > 100$. From the point of view of astronomy and astrophysics also new regimes are explored: (i) the occurrence of gravitational collapse to a black hole from a critical mass core of mass $M\agt 10M_\odot$, which clearly differs from the values of the critical mass encountered in the study of stars "catalyzed at the endpoint of thermonuclear evolution" (white dwarfs and neutron stars); (ii) the extremely high efficiency of the spherical collapse to a black hole, where almost $99.99\%$ of the core mass collapses leaving negligible remnant; (iii) the necessity of developing a fine tuning in the final phases of thermonuclear evolution of the stars, both for the star collapsing to the black hole and the surrounding ones, in order to explain the possible occurrence of the "induced gravitational collapse". New regimes are as well encountered from the point of view of nature of GRBs: (I) the basic structure of GRBs is uniquely composed by a proper-GRB (P-GRB) and the afterglow; (II) the long bursts are then simply explained as the peak of the afterglow (the E-APE) and their observed time variability is explained in terms of inhomogeneities in the interstellar medium (ISM); (III) the short bursts are identified with the P-GRBs and the crucial information on general relativistic and vacuum polarization effects are encoded in their spectra and intensity time variability. A new class of space missions to acquire information on such extreme new regimes are urgently needed.

The recent analysis of the cosmic microwave background data carried out by the WMAP team seems to show that the sum of the neutrino masses is <0.7 eV. However, this result is not model-independent, depending on precise assumptions on the cosmological model. We study how this result is modified when the assumption of perfect lepton symmetry is dropped out.

This is a summary of the talks presented at the Rome GRB meeting by C.L. Bianco and R. Ruffini. It was shown that by respecting the relative space-time transformation paradigm (RSTT), important inferences are possible in the new physics occurring in the energy sources of GRBs, on the structure of the bursts as well as on the composition of the interstellar matter surrounding the source. All current theoretical models of GRBs, by neglecting the implementation of this paradigm, lack the fundamental cognitive tools relating the physical nature of the source to the received GRBs light signals.

By integrating the relativistic hydrodynamic equations introduced by Taub we have determined the exact EQuiTemporal Surfaces (EQTSs) for the Gamma-Ray Burst (GRB) afterglows. These surfaces are compared and contrasted to the ones obtained, using approximate methods, by Panaitescu & Meszaros (1998), Sari (1998), Granot et al. (1999).

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, V. Gurzadyan, S.-S. Xue, On the instantaneous spectrum of Gamma-Ray Bursts, Int.J.Mod.Phys. D13, 843-852, 2004

A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave giving rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a di erent viewing angle in the past light cone of the observer. Therelativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the ective emitting area in the shock wave front. A self consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit

R. Ruffini, C.L. Bianco, P. Chardonnet, F. Fraschetti, V. Gurzadyan, S.S. Xue, Emergence of a filamentary structure in the fireball from GRB spectra, 9 pages, 3 figures, to appear on International Journal of Modern Physics D

It is shown that the concept of a fireball with a definite filamentary structure naturally emerges from the analysis of the spectra of Gamma-Ray Bursts (GRBs). These results, made possible by the recently obtained analytic expressions of the equitemporal surfaces in the GRB afterglow, depend crucially on the single parameter R describing the e ective area of the fireball emitting the X- and gamma ray radiation. The X- and gamma ray components of the afterglow radiation are shown to have a thermal spectrum in the co-moving frame of the fireball and originate from a stable shock front described self-consistently by the Rankine-Hugoniot equations. Precise predictions are presented on a correlations between spectral changes and intensity variations in the prompt radiation verifiable, e.g., by the Swift and future missions. The highly variable optical and radio emission depends instead on the parameters of the surrounding medium. The GRB 991216 is used as a prototype for this model. Keywords: black hole physics  gamma rays: bursts  gamma rays: theory  ISM: clouds  ISM: structure  radiation mechanisms: thermal 

R. Ruffini, C.L. Bianco, On the exact analytic expressions for the equitemporal surfaces in Gamma-Ray Burst afterglows, Astrophysical Journal, vol. 620, pp. L23-L26, ISSN: 0004-637X

We have recently shown (see Bianco & Ruffini 2004) that marked differences exist between the EQuiTemporal Surfaces (EQTSs) for the Gamma-Ray Burst (GRB) afterglows numerically computed by the full integration of the equations of motion and the ones found in the current literature expressed analytically on the grounds of various approximations. In this Letter the exact analytic expressions of the EQTSs are presented both in the case of fully radiative and adiabatic regimes. The new EQTS analytic solutions validate the numerical results obtained in Bianco & Ruffini (2004) and offer a powerful tool to analytically perform the estimates of the physical observables in GRB afterglows.

R. Ruffini, F. Fraschetti, L. Vitagliano, S.-S. Xue, Observational signatures of an electromagnetic overcritical gravitational collapse, 11 pages, 3 figures, to appear on Int.J.Mod.Phys.D

We present theoretical predictions for the spectral, temporal and intensity signatures of the electromagnetic radiation emitted during the process of the gravitational collapse of a stellar core to a black hole, during which electromagnetic field strengths rise over the critical value for $e^+e^-$ pair creation. The last phases of this gravitational collapse are studied, leading to the formation of a black hole with a subcritical electromagnetic field, likely with zero charge, and an outgoing pulse of initially optically thick $e^+e^-$-photon plasma. Such a pulse reaches transparency at Lorentz gamma factors of $10^2$--$10^4$. We find a clear signature in the outgoing electromagnetic signal, drifting from a soft to a hard spectrum, on very precise time-scales and with a very specific intensity modulation. The relevance of these theoretical results for the understanding of short gamma-ray bursts is outlined.

R. Ruffini, M.G. Bernardini, C.L. Bianco, P. Chardonnet, F. Fraschetti,S.-S. Xue, A New Astrophysical "Triptych": GRB030329/SN2003dh/URCA-2, 4 pages, 1 figure, to appear in the Proceedings of the Los Alamos "Gamma Ray Burst Symposium" in Santa Fe, New Mexico, September 8-12 2003 (AIP Conf. Ser.), CHAPTER: GRB030329

We analyze the data of the Gamma-Ray Burst/Supernova GRB030329/SN2003dh system obtained by HETE-2 (GCN [1]), R-XTE (GCN [2]), XMM (Tiengo et al. [3]) and VLT (Hjorth et al. [4]) within our theory (Ruffini et al. [5] and references therein) for GRB030329. By fitting the only three free parameters of the EMBH theory, we obtain the luminosity in fixed energy bands for the prompt emission and the afterglow (see Fig.1). Since the Gamma-Ray Burst (GRB) analysis is consistent with a spherically symmetric expansion, the energy of GRB030329 is E = 2.1 * 10^{52} erg, namely ~ 2 * 10^3 times larger than the Supernova energy. We conclude that either the GRB is triggering an induced-supernova event or both the GRB and the Supernova are triggered by the same relativistic process. In no way the GRB can be originated from the supernova. We also evidence that the XMM observations (Tiengo et al. [3]), much like in the system GRB980425/SN1998bw (Ruffini et al. [6], Pian et al. [7]), are not part of the GRB afterglow, as interpreted in the literature (Tiengo et al. [3]), but are associated to the Supernova phenomenon. A dedicated campaign of observations is needed to confirm the nature of this XMM source as a newly born neutron star cooling by generalized URCA processes.

R. Ruffini, A. Corsi, M.G. Bernardini, C.L. Bianco, P. Chardonnet, F. Fraschetti,S.-S. Xue, GRB 970228 Within the EMBH Model, 4 pages, 1 figure, to appear in the Proceedings of the Los Alamos "Gamma Ray Burst Symposium" in Santa Fe, New Mexico, September 8-12 2003 (AIP Conf. Ser.), CHAPTER: GRB Connection to Supernovae

We consider the gamma-ray burst of 1997 February 28 (GRB 970228) within the ElectroMagnetic Black Hole (EMBH) model. We first determine the value of the two free parameters that characterize energetically the GRB phenomenon in the EMBH model, that is to say the dyadosphere energy, $E_{dya}=5.1\times10^{52}$ ergs, and the baryonic remnant mass $M_{B}$ in units of $E_{dya}$, $B=M_{B}c^{2}/E_{dya}=3.0\times10^{-3}$. Having in this way estimated the energy emitted during the beam-target phase, we evaluate the role of the InterStellar Medium (ISM) number density (n$_{ISM}$) and of the ratio ${\cal R}$ between the effective emitting area and the total surface area of the GRB source, in reproducing the observed profiles of the GRB 970228 prompt emission and X-ray (2-10 keV energy band) afterglow. The importance of the ISM distribution three-dimensional treatment around the central black hole is also stressed in this analysis.

R. Ruffini, F. Fraschetti, M.G. Bernardini, C.L. Bianco, P. Chardonnet,S.-S. Xue, The GRB980425-SN1998bw Association in the EMBH Model   4 pages, 1 figure, to appear in the Proceedings of the Los Alamos "Gamma Ray Burst Symposium" in Santa Fe, New Mexico, September 8-12 2003 (AIP Conf. Ser.)

Our GRB theory, previously developed using GRB 991216 as a prototype, is here applied to GRB 980425. We fit the luminosity observed in the 40--700 keV, 2--26 keV and 2--10 keV bands by the BeppoSAX satellite. In addition the supernova SN1998bw is the outcome of an ``induced gravitational collapse'' triggered by GRB 980425, in agreement with the GRB-Supernova Time Sequence (GSTS) paradigm (\citet{lett3}). A further outcome of this astrophysically exceptional sequence of events is the formation of a young neutron star generated by the SN1998bw event (\citet{cospar02}). A coordinated observational activity is recommended to further enlighten the underlying scenario of this most unique astrophysical system.

R. Ruffini, Extracting energy from black holes: Short-GRBs, Long-GRBs and GRB afterglows, 14 pages, 8 figures, to appear in "Frontier in Astroparticle Physics and Cosmology", Proceedings of the 6th RESCEU International Symposium held on 4-7 November 2003, Tokyo, Japan, Universal Academy Press

The extractable energy from a black hole, as origin of the Gamma-Ray Burst (GRB) phenomenon is reviewed.

R. Ruffini, P. Chardonnet , A. Mattei,S.S. Xue, The emission of Ultra High Energy Cosmic Rays from Electro-Magnetic Black Holes    10 pages, 4 figures, to appear on Int.J.Mod.Phys.D

R. Ruffini, L. Vitagliano, S.S. Xue, On Dynamical formation of Dyadosphere, to appear in the Proceeding of Xth Marcel Grossmann Meeting, ICRA,CBPF, Rio de Janeiro, July 20-26, 2003, Brazil

We discuss the evolution of the plasma around a collapsing star core endowed with a net electric charge described by the Reissner-Norstrom geometry. The star is assumed to reach values of the electric field larger than the Heisenberg-Euler-Schwinger critical value for pair production. We consider the dynamical formation of the Dyadosphere.
We show that the plasma near the event horizon falls into the black hole, while the outer plasma expands reaching ultrarelativistic velocities.

R. Ruffini, L. Vitagliano, S.S. Xue, Electron-positron-photon plasma around a collapsing massive star, Abstracts of the Xth Marcel Grossmann Meeting, ICRA, CBPF, Rio de Janeiro, July 20-26, 2003, Brazil

R. Ruffini, M.G. Bernardini, C.L. Bianco, P. Chardonnet, F. Fraschetti, V. Gurzadyan, L. Vitagliano, S.S. Xue, The Blackholic energy: long and short Gamma-Ray Bursts (New perspectives in physics and astrophysics from the theoretical understanding of Gamma-Ray Bursts, II), 86 pages, 50 figures, to appear on the "Proceedings of the XIth Brazilian School of Cosmology and Gravitation", AIP, in press

[...] We turn then to the theoretical developments in the short GRBs: we first report some progress in the understanding the dynamical phase of collapse, the mass-energy formula and the extraction of blackholic energy which have been motivated by the analysis of the short GRBs. In this context progress has also been accomplished on establishing an absolute lower limit to the irreducible mass of the black hole as well as on some critical considerations about the relations of general relativity and the second law of thermodynamics. We recall how this last issue has been one of the most debated in theoretical physics in the past thirty years due to the work of Bekenstein and Hawking. Following these conceptual progresses we analyze the vacuum polarization process around an overcritical collapsing shell. We evidence the existence of a separatrix and a dyadosphere trapping surface in the dynamics of the electron-positron plasma generated during the process of gravitational collapse. We then analyze, using recent progress in the solution of the Vlasov-Boltzmann-Maxwell system, the oscillation regime in the created electron-positron plasma and their rapid convergence to a thermalized spectrum. We conclude by making precise predictions for the spectra, the energy fluxes and characteristic time-scales of the radiation for short-bursts. If the precise luminosity variation and spectral hardening of the radiation we have predicted will be confirmed by observations of short-bursts, these systems will play a major role as standard candles in cosmology. These considerations will also be relevant for the analysis of the long-bursts when the baryonic matter contribution will be taken into account.

R. Ruffini, Maria Grazia Bernardini, Carlo Luciano Bianco, Pascal Chardonnet, Federico Fraschetti, Vahe Gurzadyan, Luca Vitagliano, S.S. Xue, Black hole physics and astrophysics: The GRB-Supernova connection and URCA-1 - URCA-2, 55 pages, 31 figures, to appear in the "Proceedings of the 10th Marcel Grossmann Meeting", Rio de Janeiro, July 20-26, 2003, World Scientific, in press

We outline the confluence of three novel theoretical fields in our modeling of Gamma-Ray Bursts (GRBs): 1) the ultrarelativistic regime of a shock front expanding with a Lorentz gamma factor $\sim 300$; 2) the quantum vacuum polarization process leading to an electron-positron plasma originating the shock front; and 3) the general relativistic process of energy extraction from a black hole originating the vacuum polarization process. There are two different classes of GRBs: the long GRBs and the short GRBs. We here address the issue of the long GRBs. [...] We are specially interested, in this report, to a subclass of long GRBs which appear to be accompanied by a supernova explosion. We are considering two specific examples: GRB980425/SN1998bw and GRB030329/SN2003dh [...].

R. Ruffini, Charges in gravitational fields: from Fermi, via Hanni-Ruffini-Wheeler, to the "electric Meissner effect", 25 pages, 17 figures, to appear on the Proceedings of "Analysis, manifolds and geometric structures in physics", International Conference in Honour of Y. Choquet-Bruhat, Isola d'Elba June 24th-26th, 2004

Recent developments in obtaining a detailed model for gamma ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordstrom black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner-Nordstrom black hole similar to the Meissner effect for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler. PACS 04.20  . PACS 04.20

The issue of the possible presence or absence of jets in GRBs is here re-examined for GRB991216, which has a claimed half-opening beaming angle of $\vartheta_\circ=3^\circ$. We compare and contrast our theoretically predicted afterglow luminosity in the 2--10 keV band for spherically symmetric versus jetted emission. Jetted emission can be excluded and data analysis confirms spherical symmetry. These theoretical fits are expected to be largely improved by the forthcoming data of the Swift mission. In addition to the source GRB991216, our model has been applied successfully, assuming spherical symmetry, to GRB980519, GRB980425, GRB030329 and to GRB970228.