riassunto2

Speaker_	Aliev, Alikram Nuhbalaoglu
Talk_	Epicyclic Frequencies and Resonant Phenomena Near Black Holes: The Current Status
Abstract_	\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}