ABSTRACTS

1. "Exactly solvable ansatz of Einstein-Maxwell Equations".
An outline of the general theory of integrability of the Einstein-Maxwell equations will be given.

2. "On the equilibrium state for two charged masses in General Relativity".
The exact stationary solution of the Einstein-Maxwell equations representing the equilibrium state of two Reissner-Nordstrom objects will be described.

3. "On the existence of black hole evaporation"
A new arguments will be presented confirming the point of view that a Schwarzschild black hole does not radiate.

The Dark Matter Universe

Dark matter is a long standing puzzle starting from Le Verrier with his discovery of Neptune in 1846 as a perturbation of Uranus. Our Galaxy is surrounded by an extended halo of unseen material. So far undetected, that dark matter induces a flat rotation curve in the Galactic plane.
Its presence has been noticed since many decades. However, its nature is still unknown. The dark matter problem consists simply, in the existence of invisible mass showing its presence by gravitational effects. Now, it is widely accepted that dark matter exists. In fact, there is evidence for dark matter on scales from galaxy to the cluster of galaxies and to the whole Universe itself. Zwicky measured the dispersion velocity in the Coma cluster and found that the dynamical mass was hundred times more than the luminosity mass. Moreover, the dark matter seems essential: the growth of structure in the Universe by hierachical merging of the dark matter halo is a master piece of moderm cosmology.
Recently, WMAP has established the presence of non baryonic dark matter with the density reported in terms of critical density of order 23%.
This is now the standard value of the modern cosmology for dark matter density.

Scattering problems in rotating astrophysical and acoustic black holes: general theory and numerical techniques

In this lecture the problem of scattering of fields of different helicity on black holes on Nature is presented. 
After a rapid review of Teukolsky formalism applied to rotating Kerr black holes, modern numerical methods developed for these problems are introduced, i.e. constrained evolution schemes, excision and advanced finite element methods.
The formalism is applied to ordinary hydrodynamics then for studying rotating acoustic black. Analogies with astrophysical black holes are discussed, with particular attention to superradiant effects.

The electro-weak model inferred from a Kaluza-Klein space-time

We present the geometrization of the electro-weak model bosonic component in a 7-dimensional and in a 8-dimensional space-time manifold through a Kaluza-Klein approach, then we introduce spinorial matter fields and we achieve the conservation of gauge charges and the geometrization of gauge connections; finally through a scalar field we are able to reproduce the spontaneous symmetry breaking mechanism.

"Motion, Radiation and Timing of Compact Binaries"

Selfgravitating systems. From Virial theorem to Hydrodynamics

Charged massive particle at rest in the field of a Reissner-Nordstr\"om black hole

 The interaction of a Reissner-Nordstr\"om black hole and a charged massive particle is studied in the framework of perturbation theory, following the approach of Zerilli.
The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields at first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicitly by closed form expressions.
The relations between these approximated solutions and the corresponding exact two-body solutions belonging to the Weyl class are discussed too.

Chaotic Stellar Systems

During the last decades the essential role of chaos in the dynamics of star clusters and galaxies has become evident. I will review some of the achieved results both in theoretical and numerical studies, along with the elements of theory of dynamical systems and mentioning of certain open problems.

Emerging Gravity from Defects in World Crystal

I show that the principles of minimal electromagnetic and gravitational couplings can be d e r i v e d from a simple nonholonomic mapping principle. By mapping flat space into a space with defects, I create spacetimes with curvature and torsion as a scenario for gravitational theories. The Riemann space of Einstein's theory arises from a "world crystal" with defects.

Relativistic astronomical reference systems and their applications

General relativity theory plays a very important role in modern astronomy. For currently available and envisaged accuracies a clear relativistic desciption of all physical processes contributing to an observation is indispensable. These three lectures are intended to give an introduction to the modern theory of relativistic modelling of high-accuracy astronomical observations. Both theoretical foundations of the modelling (standard relativistic astronomical reference systems) and practical applications to a number of particular kinds of observations will be discussed.

Lecture 1: Astronomical observations in relativity: the need for relativistic astronomical reference systems
Lecture 2: Relativistic astronomical reference systems: advanced properties
Lecture 3: Relativistic modelling of some particular kinds of observations

Exploiting binary pulsars as laboratories of gravity theories

A new era in fundamental physics began when pulsars where discovered in 1967. They are useful tools for a wide variety of physical and astrophysical problems, in particular for the study of theories of relativistic gravity. Being precise cosmic clocks, pulsars take us beyond the weak-field limit of the solar-system. Their contribution is crucial as no test can be considered to be complete without probing the strong-field realm of gravitational physics by finding and timing pulsars. In this review, I will review the observations of pulsars and explain some of the most important applications of millisecond pulsar clocks in the study of gravity. Recent discoveries such as the double pulsar, and prospects of finding a pulsar-black hole system are discussed.

Optical extension of the ICRF to faint stars

After discussing methods and techniques for extending (densifying) the ICRF to faint magnitudes in the optical domain, this lecture will illustrate the importance of such work with examples ranging from extra-galactic astronomy, to Galactic structure, and from high energy astrophysics to supporting on going and future space missions.

Linear Evolution of Cosmological Density Perturbations in Mixed Dark Matter Models

The growth of cosmological density perturbations in a Universe filled by both hot dark matter (HDM) and cold dark matter (CDM) proceeds in a different way than in pure CDM Universe. In this so-called Mixed Dark Matter (MDM) models, the presence of a HDM component, like neutrinos, causes the damping of small-scale density perturbations. We will show how the shape of the power spectrum of matter perturbations is influenced by the presence of the HDM component, and most notably by the mass and spectral distribution of the HDM particle, and how this can be used to constrain neutrino properties.

Radiative processes around black hole horizons in X-ray binaries.

In this lecture, we will first make an overview of the observed spectral and timing properties of X-ray binaries, stressing peculiarly on the observables which seems to be directly related to the close environment of the black holes.
Then, we will see briefly how is described theoretically the flow which is accreted by the black hole, producing the tremendous amount of X-rays we observe from these binary systems. This will give us a view of what is physically understood in these regions, and which open questions remain.
Starting from this point, we will describe, after a brief introduction to Monte-Carlo simulations, the new panorama we imagine of what happen close to the black hole horizon in X-ray binary, panorama arising from both recent numerical simulations of radiative processes in the Schwarzschild metric and joint theoretical approaches.

Kaluza-Klein theories: Lorentz gauge theories and the Electro-Weak model.

In the framework of a 5-dimensional Kaluza –Klein theory, the Electro-Weak Model will be geometrized, the extra-dimension providing the proper degrees of freedom.
U (1) weak hyper-charge Abelian gauge field will be identified in the off diagonal component of the metric tensor, as in usual KK theories. Matter spinorial fields will be extended to 5 dimensions in accordance with the structure of the 5-D manifold: chirality will be a direct result of the 5-D Dirac algebra, different ‘’particles’’ will be described in relation to different periodicity properties of the ‘’motion’’ along the extra-ring, and the 5^th component of the momentum will be proved to be a conserved quantity coinciding to the weak hyper-charge.
A gauge theory for the Local Lorentz Group will be established in Riemann-Cartan spaces: the Ricci coefficients will be explained to be inconsistent with the definition of a gauge field, as they are not primitive objects and define the bein projection of the rotational parameter, thus clarifying the need of such a geometrical background. Conserved quantities will be found in the comparison of gauge charges and the bein projection of the angular momentum tensor: in 5 dimensions, Lorentz group will be defined consistently with the features of the manifold, and SU (2) weak isospin generators will be inferred from the extra-dimensional conserved current coupled to the pertinent gauge field (the proper extra-dimensional bein projection of the contortion field).
After dimensional reduction, the Electro-Weak model will be perfectly restored according to the different geometrical origin of the two gauge symmetries.   

Astronomy with ultra-high energy cosmic ray

The study of propagation of ultra high energy cosmic rays is a key  step in order to unveil the secret of the origin of Ultra High Energy  Cosmic Rays. I have developed a complete UHECR cosmic ray propagation  code using energy losses. I have studied the influence of the  magnetic field of the galaxies. I have used the most complete galaxy  catalog up to now: the LEDA catalog with order of 60.000 galaxies  inside 80 Mpc. In the simulations I have modeled the magnetic field  of the halo by a dipole of size of order of 100 kpc and a typical  value for B of 100nG.
The code developed is able to retro-propagate a  charge particle from the arrival points selected from AGASA data  across the galaxy field of LEDA catalog. I will present the results  of various simulations and show the influence of the galactic  magnetic halo on the UHECR propagation. Particular attention will be  done on the AGASA triplet.

Torsion as gauge theory of the Lorentz group and extensions of General Relativity in Ashtekar formalism.

Taking the Einstein-Cartan theory as starting point:
1) On one side we give some arguments for introducing an independent gauge field of the local Lorentz group and present a theory in which this role is played by the contortion field. The full picture involving gravity, torsion and spinor fields is settled down by a system of equations, which show how the source of the Yang-Mills contortion field is the density of spin of the femions. In this theory the contortion acquires a propagating character, moreover the Fermi-like interaction term of the Einstein-Cartan theory is substituted by the usual minimal gauge interaction.
2) On the other side, after a brief introduction of the Ashtekar-Barbero-Immirzi formulation of General Relativity in the Lagrangian Holst formalism, we show that in order to obtain the Einstein-Cartan as effective theory a non-minimal interaction term must be added to the spinor action. The non-minimal interaction together with the Holst modification to the Hilbert-Palatini action reconstruct the Nieh-Yan topological term. Finally we show that the total action for the gravity-fermions coupled system can be reduced to a weighted sum of self and anti-self dual Ashtekar-Romano-Tate action with different weights depending on the Immirzi parameter, this allows us to calculate the constraints of the theory in a very simple way; they come out to be polynomial, hopefully opening the way to the inlusion of spinor matter in the framework of non-perturbative quantum gravity with real connections.

Tuesday 7      Principle of fundamental astrometry and application to the construction of an inertial reference frame.
Wednesday 8 The establishment of the ICRF with extra-galactic sources, its properties, maintenance and evolution. 

The realisation of a practical inertial frame from stellar directions has been the major objective of fundamental astronomy for many years. I will recall the basic principle behind this realisation up to the last version of the optical frame before Hipparcos, and then describe the current paradigm based on the extra galactic sources with the current ICRF (International Celestial Reference Frame) built in the framework of relativistic prescription. In the last part I will discuss the future evolution of the realisation of the inertial frame with the next ESA astrometry mission Gaia.

1. The structure of the geometry of spacetime in nonlinear field theories

 In recent years there has been a growing interest in models that mimic in the laboratory some features of gravitation. The actual realization of these models relies on systems that are very different in nature: ordinary viscous fluids, superfluids, flowing dielectrics, non linear electromagnetism and Bose-Einstein condensates. The basic feature shared by these systems is that the behavior of the fluctuations around a background solution is governed by an "effective metric". We will analyse the case of non linear Electrodynamics.

2. Cosmological effects of nonlinear field theories

Linear  Electrodynamics considered as a source of the classical Einstein field equations leads to the singular isotropic Friedmann solutions for the cosmological metric. This singular behavior is not present if non linear terms are added to Maxwell lagrangian. We will analyse also the case of recent proposals of considering non linear field theories for scalar fields  as a possible  explanation of the acceleration of the universe.

Thanks to the development of space technologies, space around Earth has become an important workbench for the experimental tests of gravitation theories (in particular Einstein geometrodynamics). This effort also yields practical applications, as shown by GPS satellite navigation technology. Following a general introduction to these topics, recent results on LAGEOS satellites will be presented. The analysis of the orbits of these satellites, built for geophysical and geodynamical applications, opens the way to important tests of Einstein theory, in particular the well-known phenomenon of dragging of inertial frames around a rotating body (Lense-Thirring effect). Its measurement will be discussed, together with some geophysical results.

Travelling with Einstein and Maxwell to Microland

In this talk I will ask a seemingly innocent question which is almost never addressed by modern physicists: What is the Einstein-Maxwell field of an electron? This is perhaps the single most important question when we try to understand nature! I will analyze this problem from the point of view of the multipole structure of Einstein-Maxwell fields. 
It will be argued that contrary to the commonly held view, gravity cannot be safely neglected at the keV/Mev energy scales of nuclear and electron physics. It is also argued that quantum effects do not alter this conclusion. Although the gravitational force itself is weak, there can be induced corrections (via the Einstein-Maxwell equations) to the Coulomb field which are observable. 
In particular, from the simplest solution of the Einstein- Maxwell equations (Kerr-Newman) one may predict that the electron has a measurable electric quadrupole moment with the value -124 barns. A non-zero value of the electric quadrupole for the electron (or the proton) would be a clear signature of curvature since spin one half particles cannot carry a quadrupole moment in flat space by the Wigner-Eckart theorem.

A Lagrangian for the dark side of the universe.

The inhomogeneity patterns of the Cosmic Microwave Background as well as the newly discovered accelerated expansion are usually treated by means of a number of fields, featuring dark energy, quintessence etc. Here we show that using a simple twofold analogy with ordinary physical phenomena, such as the internal friction of a fluid and the induced metric effects of defects in continua, it is possible to build a Lagrangian and a corresponding metric theory leading to inflation and to an accelerated expansion of the space time, with no further need for anything "dark".

Wedenesday 15
Relativistic theory of angular distances

We recall the relativistic definition of the direction of a light ray in the 3-space relative to an arbitrary observer. We show how to obtain the general expression of the angular distance between two sources as measured  by this observer. The general formula is applied to the most frequently used approximation schemes in metric theories of gravity.

Thursday 16
The world function as a tool for relativistic astrometry

Almost all of the papers devoted to relativistic astrometry are based on the solution of the null geodesic equations. However, the deflection of light rays can be calculated without knowing the null geodesics if one is able to determine the bifunction giving half the squared geodesic distance between two arbitrary points-events. After a review of the main properties of this bifunction, which has been called the “ world function” by Synge, we present different methods of carrying out its calculation. Then, we give some examples illustrating these methods. In particular, we show how to calculate the contribution of each mass-multipole term to light deflection in a stationary gravitational field.

Spectral and Timing Signatures of Neutron Star and Black Hole Sources

Kinetic and thermal equilibria in the pair plasma

There is a growing evidence that relativistic plasma appears in various astrophysical systems such as accretion discs, AGNs, GRBs.
The reivew of basic properties of this plasma will be provided giving particular attention to the case of purely electron-positron-photon plasma. We will discuss general conditions under which the plasma can be considered in equilibrium, distinguishing between the concepts of kinetic and thermal equilibrium. As an illustration of this discussion two scenarios within the fireball model of GRBs will be considered, treating in a different way the three particle interactions in the plasma.

 Short gamma ray bursts of an electromagnetic overcritical gravitational collapse

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 shown.