Quasinormal modes of Reissner-Nordström-anti-de Sitter black holes: scalar, electromagnetic and gravitational perturbations

Abstract

We study scalar, electromagnetic and gravitational perturbations of a Reissner-Nordström-anti-de Sitter (RN-AdS) spacetime, and compute its quasinormal modes (QNM&#39;s). We confirm and extend results previously found for Schwarzschild-anti-de Sitter (S-AdS) black holes. For ``large&#39;&#39; black holes, whose horizon is much larger than the AdS radius, different classes of perturbations are almost exactly {\it isospectral}; this isospectrality is broken when the black hole&#39;s horizon radius is comparable to the AdS radius. We provide very accurate fitting formulas for the QNM&#39;s, which are valid for black holes of any size and charge $Q<Q_{ext}/3$. Electromagnetic and axial perturbations of large black holes are characterized by the existence of pure-imaginary (purely damped) modes. The damping of these modes tends to infinity as the black hole charge approaches the extremal value; if the corresponding mode amplitude does not tend to zero in the same limit, this implies that {\it extremally charged RN-AdS black holes are marginally unstable}. This result is relevant in view of the AdS/CFT conjecture, since, according to it, the AdS QNM&#39;s give the timescales for approach to equilibrium in the corresponding conformal field theory.