Quasinormal modes of black holes: From astrophysics to string theory

Abstract

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten years in string theory, brane-world models and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes (QNMs), allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, AdS/CFT interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

Lifshitz quasinormal modes and relaxation from holography

“…For d = 3, z = 2 this equation coincides with the one found in [12]. For reviews on this topic we recommend [13,14]. A summary of previously obtained analytic and numerical solutions of quasinormal modes of spin-zero fields, making usage of various bulk actions, entails: d = 2, z = 3 in New Massive Gravity (NMG) [15], d ≥ 4, z = 2 in a R 2 gravity setting [16] and d ≥ 2, z = 2 in a R 3 gravity setting [17].…”

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions

“…It is well known that the QNF are determined by the parameters of the black hole as the mass, charge, and angular momentum. For more details see the extensive reviews [1]- [4].…”

“…In addition to the QNF of black holes that are relevant for astrophysics, the QNF of other gravitational backgrounds have been calculated. In particular, motivated by the AdS-CFT correspondence, the QNF of asymptotically anti-de Sitter black holes are thoroughly studied (see references [5]- [28] for some examples and the reviews [3,4] for additional references), since according to the AdS-CFT correspondence the QNF of asymptotically anti-de Sitter black holes are related to the hydrodynamic properties of a gauge theory fluid.…”

“…In many references are used perturbative or numerical methods to calculate the QNF of the black holes (see the reviews [1]- [4] and references therein). Nevertheless for some spacetimes their QNF are computed exactly and it should be noted that many of these gravitational systems are lower dimensional.…”

A scattering approach to some aspects of the Schwarzschild black hole

“…for frequencies of order ω ≫ (2M ) −1 , where M is the mass of the Schwarzschild BH and thus limits the analysis to a scattering description of weakly damped QNM, formally associated to high angular momenta. Thus, highly damped QNM [6], Hawking radiation, and more generally, the physics near the BH horizon seems to be out of such framework. Nevertheless, in this paper, we claim that one could have a physical description of the near horizon physics without using any conformal field theories but by focusing, precisely, on the scattering of an ingoing s-wave by the non null barrier of the Regge-Wheeler potential of the Schwarzschild BH.…”