Quasinormal modes of Reissner-Nordstr\"om-anti-de Sitter black holes: scalar, electromagnetic and gravitational perturbations

TL;DR

This paper analyzes scalar, electromagnetic, and gravitational quasinormal modes of Reissner-Nordström-anti-de Sitter black holes, revealing near-isospectrality for large black holes and potential marginal instability at extremal charge, with implications for AdS/CFT correspondence.

Contribution

It extends previous results on Schwarzschild-AdS black holes to charged RN-AdS black holes, providing accurate QNM formulas and insights into stability and isospectrality.

Findings

Large black holes exhibit near-isospectral perturbations.

Pure-imaginary damping modes exist for electromagnetic and axial perturbations.

Extremally charged RN-AdS black holes may be marginally unstable.

Abstract

We study scalar, electromagnetic and gravitational perturbations of a Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) spacetime, and compute its quasinormal modes (QNM's). We confirm and extend results previously found for Schwarzschild-anti-de Sitter (S-AdS) black holes. For ``large'' 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's horizon radius is comparable to the AdS radius. We provide very accurate fitting formulas for the QNM'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's give the timescales for approach to equilibrium in the corresponding conformal field theory.