ar X iv : h ep - t h / 02 05 14 2 v 1 1 4 M ay 2 00 2 On quasinormal modes of small Schwarzschild - Anti - de - Sitter black hole
نویسنده
چکیده
We compute the quasinormal modes associated with decay of the massless scalar filed around a small Schwarzschild-Anti-de-Sitter black hole. The computations shows that when the horizon radius is much less than the anti-de-Sitter radius, the imaginary part of the frequency goes to zero as r d−2 + while the real part of ω decreases to its minimum and then goes to d − 1. Thus the quasinormal modes approach the usual AdS modes in the limit r + → 0. This agrees with suggestions of Horowitz et al (Phys.Rev. D62 024027 (2000)). Original interest to quasinormal modes of black holes arose since they are the characteristics of black holes which do not depend on initial perturbations and are functions of a black hole parameters only. At present, this interest is renewed since the QN frequencies are in the suggested region of the gravitational wave detectors which are under construction. In general QNM's are important in black holes dynamics and appear in such processes as collisions of two black holes, decay of different fields in a BH background. All this motivated the investigation of the QNM of black holes in asymptotically flat space-time (see [1] for a recent review). The quasinormal modes of asymptotically de-Sitter black holes were studied in [2],[3]. Recently an unexpected application of quasi-normal modes have appeared due to the AdS/CFT correspondence [4]: it proved out that a large black hole in AdS space corresponds to an approximately thermal state in the CFT, and, thereby, perturbation of the black hole corresponds to the perturbation of the above thermal state, while the decay of the perturbation can be associated with the return to thermal equilibrium. Thus the QN frequencies give us the thermalization timescale which is very hard to compute directly. Quasinormal modes for different types of perturbations of black holes in AdS space have been studied recently in a lot of papers [5]-[14]. Black holes are considered to be small (large), when its horizon radius is much smaller (larger) then the anti-de-Sitter radius. When computing the QN frequencies associated with the decay of massless scalar field in the background of small SAdS BH a striking conjecture with the black hole critical phenomena was found: ω Im is proportional to BH radius r + to high accuracy, and the slope of the line ω Im to the r + axis, 2.66, turned out to be very close to the …
منابع مشابه
ar X iv : h ep - t h / 05 03 02 9 v 2 1 A pr 2 00 5 Scalar field perturbations of the Schwarzschild black hole in the Gödel Universe
We investigate the scalar field perturbations of the 4+1-dimensional Schwarzschild black hole immersed in a Gödel Universe, described by the Gimon-Hashimoto solution. This may model the influence of the possible rotation of the Universe upon the radiative processes near a black hole. In the regime when the scale parameter j of the Gödel background is small, the oscillation frequency is linearly...
متن کاملar X iv : h ep - t h / 05 02 10 9 v 1 1 1 Fe b 20 05 The Self - Gravitational Corrections as the Source for Stiff Matter on the Brane in SAdS 5 Bulk
A D3− brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. Taking into account the semi-classical corrections to the black hole entropy that arise as a result of the self-gravitational effect, and employing the AdS/CFT correspondence, we obtain the self-gravitational correction to the first Friedmann-like equation. ...
متن کاملX iv : g r - qc / 0 30 50 37 v 1 9 M ay 2 00 3 Quasinormal frequencies of Schwarzschild black holes in anti - de Sitter spacetimes : A complete study on the asymptotic behavior
We present a thorough analysis for the quasinormal (QN) behavior, associated with the decay of scalar, electromagnetic and gravitational perturbations, of Schwarzschild− anti-de Sitter black holes. As it is known the anti-de Sitter (AdS) QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the bl...
متن کاملar X iv : g r - qc / 0 50 20 46 v 2 1 1 Fe b 20 05 Gravitational quasinormal modes for Kerr Anti - de Sitter black holes
We investigate the quasinormal modes for gravitational perturbations of rotating black holes in four dimensional Anti-de Sitter (AdS) spacetime. The study of the quasinormal frequencies related to these modes is relevant to the AdS/CFT correspondence. Although results have been obtained for Schwarzschild and Reissner-Nordstrom AdS black holes, quasinormal frequencies of Kerr-AdS black holes are...
متن کاملar X iv : h ep - t h / 04 04 04 7 v 2 18 A ug 2 00 4 Quasinormal modes in pure de sitter spacetimes
We have studied scalar perturbations as well as fermion perturbations in pure de Sitter space-times. For scalar perturbations we have shown that well-defined quasinormal modes in d-dimensions can exist provided that the mass of scalar field m > d−1 2l . The quasinormal modes of fermion perturbations in three and four dimensional cases have also been investigated. We found that different from ot...
متن کامل