MG11 
Talk detail
 

 Participant 

Institution

Session

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Abstract

A. N. Aliev, Self-Dual Fields on the Space of a Kerr-Taub-bolt Instanton

\documentclass[aps,report]{revtex4} \begin{document} \title{\Large \bf Self-Dual Fields on the Space of a Kerr-Taub-bolt Instanton} \author{\large A. N. Aliev} \affiliation{ Feza G\"ursey Institute, P.K. 6 \c Cengelk\" oy, 81220 Istanbul, Turkey} \author{\large Cihan Sa\c{c}l\i o\u{g}lu} \affiliation{Faculty of Engineering and Natural Sciences, Sabanci University, 81474 Tuzla, Istanbul, Turkey} %\pagestyle{empty} \maketitle \noindent Gravitational instantons are usually defined as complete nonsingular solutions of the vacuum Einstein field equations in Euclidean space. One of the fundamental properties of gravitational instantons is that they can harbor self-dual gauge fields that have no effect on the metric. In other words, since the energy-momentum tensor vanishes identically for self-dual gauge fields, solutions of Einstein's equations automatically satisfy the system of coupled Einstein-Maxwell and Einstein-Yang-Mills equations. In recent years, motivated by Sen's $S$-duality conjecture, there has been some renewed interest in self-dual gauge fields living on well-known Euclidean-signature manifolds. The gauge fields were studied by constructing self-dual square integrable harmonic forms on given spaces. For instance, the square integrable harmonic two-form in self-dual Taub-NUT metrics was constructed in \cite{gibbons}, its generalization to the case of complete noncompact hyper-K\"ahler spaces was given in \cite{hitchin}. In this framework, we shall report on a new exact solution that describes the Abelian gauge fields harbored by the Kerr-Taub-bolt instanton, which is a generalized example of asymptotically flat instantons with non-self-dual curvature. We shall discuss the construction of the corresponding self-dual and anti-self-dual harmonic two-forms and show that they are square integrable on the Kerr-Taub-bolt space \cite{ac}. \begin{thebibliography}{99} \bibitem{gibbons} G. W. Gibbons, Phys. Lett. B {\bf 382}, 53 (1996) \bibitem{hitchin} N. Hitchin, Commun. Math. Phys. {\bf 211}, 153 (2000) \bibitem{ac} A. N. Aliev and C. Sa\c{c}l\i o\u{g}lu, Phys. Lett. B {\bf 632}, 725 (2006) \end{thebibliography} \end{document}

Rotating Braneworld Black Holes

\documentclass[aps,report]{revtex4} \begin{document} \title{\Large \bf Rotating Braneworld Black Holes} \author{\large A. N. Aliev} \affiliation{ Feza G\"ursey Institute, P.K. 6 \c Cengelk\" oy, 81220 Istanbul, Turkey} \maketitle \noindent Several strategies have been discussed in the literature to describe the braneworld black holes. First of all, it has been argued that if the radius of the horizon of a black hole on the brane is much smaller than the size of the extra dimensions $(\,r_{+} \ll L \,)$, the black hole, to a good enough approximation, can be described by the usual classical solutions of higher dimensional vacuum Einstein equations. In the opposite limit when ($\,r_{+} \gg L \,)$, the black hole becomes effectively four-dimensional with a finite extension along the extra dimensions. The first simple solution pertinent to the latter case in the Randall-Sundrum braneworld is based on the idea of a usual Schwarzschild metric on the brane that would look like a {\it black string} solution from the point of view of an observer in the bulk \cite{chr}. However, the black string solution exhibits curvature singularities at infinite extension along the extra dimension. In this report I shall discuss another strategy of finding an exact solution that describes black holes localized on a 3-brane in the Randall-Sundrum scenario. I shall specify the metric form induced on the 3-brane assuming a Kerr-Schild ansatz for it. With this ansatz the system of the effective gravitational field equations on the brane \cite{sms,ae1} becomes closed and the solution to this system turns out to be a Kerr-Newman type stationary axisymmetric black hole which possesses a {\it tidal} charge instead of a usual {\it electric} charge. The tidal charge has a five-dimensional origin and can be thought of as an imprint of the non-local gravitational effects from the bulk space. I shall also present a new solution that describes a rotating black hole on the brane carrying both tidal and electric charges. Finally, I shall discuss the physical properties of these solutions and their possible astrophysical consequences. \noindent The report will be based on a recent joint work with A. E. Gumrukcuoglu \cite{ae2}. \begin{thebibliography}{99} \bibitem{chr} A. Chamblin, S. W. Hawking and H. S. Reall, Phys. Rev. D {\bf 61} 065007 (2000) \bibitem{sms} T. Shiromizu, K. Maeda, and M. Sasaki, Phys. Rev. D {\bf 62}, 024012 (2000) \bibitem{ae1} A. N. Aliev and A. E. Gumrukcuoglu, Class. Quant. Grav. {\bf 21}, 5081 (2004). \bibitem{ae2} A. N. Aliev and A. E. Gumrukcuoglu, Phys. Rev. D {\bf 71}, 104027 (2005) \end{thebibliography} \end{document}

Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity

\documentclass[aps,abstarct]{revtex4} \begin{document} \title{\Large \bf Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity} \author{\large A. N. Aliev} \affiliation{Feza G\"ursey Institute, P.K. 6 \c Cengelk\" oy, 81220 Istanbul, Turkey} \maketitle \noindent Black hole solutions in higher dimensional Einstein and Einstein-Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner-Nordstrom and Kerr solutions of four-dimensional general relativity. However, higher dimensional counterpart of the Kerr-Newman solution still remains to be found analytically. Numerical solutions for some special cases in five dimensions were given in \cite{knp}. As is known, the strategy of obtaining the Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a non-rotating charged black hole. In practice, this amounts to an appropriate re-scaling of the mass parameter in the metric of uncharged black holes. In the framework of a similar approach, I shall discuss a special metric ansatz in $\,N+1\, $ dimensions and present a new analytic solution to the Einstein-Maxwell system of equations. It describes rotating charged black holes with a single angular momentum in the limit of slow rotation. I shall also present the metric for a slowly rotating charged black hole with two independent angular momenta in five dimensions. Finally, I shall discuss the gyromagnetic ratio of these black holes and show that it corresponds to the value $\,g=N-1\,$. \noindent The report will be based on recent works \cite{ali1,ali2}. \begin{thebibliography}{99} \bibitem{knp} J. Kunz, F. Navarro-Lerida and A. K. Petersen, Phys. Lett. B {\bf 614}, 104 (2005) \bibitem{ali1} A. N. Aliev, Mod. Phys. Lett. A {\bf 21}, 751 (2006) \bibitem{ali2} A. N. Aliev, hep-th/0604207 \end{thebibliography} \end{document}

Epicyclic Frequencies and Resonant Phenomena Near Black Holes: The Current Status

\documentclass[aps,report]{revtex4} \begin{document} \title{\Large \bf Epicyclic Frequencies and Resonant Phenomena Near Black Holes: The Current Status} \author{\large A. N. Aliev} \affiliation{ Feza G\"ursey Institute, P.K. 6 \c Cengelk\" oy, 81220 Istanbul, Turkey} \maketitle \noindent In the framework of general relativity the successive theory of epicyclic motion around rotating black holes for the first time was developed in \cite{ag1,ag2}. It has been shown that at the linear order in perturbations the epicyclic motion of a test particle in the equatorial plane is governed by two decoupled oscillatory-type equations. The associated frequencies of the radial and vertical oscillations were calculated in most general cases when the black hole possesses an electric charge, or it is immersed in an uniform magnetic field. It has also been pointed out that when these frequencies are in rational relation, the resonant phenomena take place in the system and the positions of some low order resonances (k=3, 4, 5, or 2:1, 3:1, 3:2) were plotted. Further, the epicyclic frequencies were used to explore the gravitational effects of periastron precession and the Lense-Thirring drag in the Schwarzschild and Kerr fields threaded by a cosmic string \cite{ag3}. In recent developments, these results were extensively used to explain the origin of high frequency Quasi-Periodic Oscillations (QPOs) seen in many cases of accreting black hole or neutron star systems \cite{mvs, taks}. In this report I shall briefly discuss the current status of the theory of epicyclic motion near black holes in comparison with recent observations of black hole systems. I shall also present some new results on non-linear resonances predicted in the theory. Finally, I shall discuss the epicyclic frequencies near braneworld black holes, as well as a constraint put by observations on the value of a tidal charge carried by these black holes. \begin{thebibliography}{99} \bibitem{ag1} A. N. Aliev and D. V. Gal'tsov, Gen. Relat. Gravit. {\bf 13}, 899 (1981) \bibitem{ag2} A. N. Aliev, D. V. Gal'tsov and V. I. Petukhov, Astr. Space Sci. {\bf 124}, 137 (1986) \bibitem{ag3} A. N. Aliev and D. V. Galt'sov, Sov. Astron. Lett. {\bf 14(1)}, 48 (1988) \bibitem{mvs} A. Merloni, M. Vietri, L. Stella and D. Bini, Mon. Not. R. Astron. Soc. {\bf 304},155 (1999) \bibitem{taks} G. Torok, M. Abramowicz, W. Kluzniak and Z. Stuchlik, Astron. Astrophys. {\bf 436}, 1 (2005) \end{thebibliography} \end{document}