Gravitational instability of simply rotating AdS black holes in higher dimensions

TL;DR

This paper investigates the stability of higher-dimensional rotating AdS black holes, finding that they are stable for slow rotation but exhibit a tiny superradiant instability when rotating rapidly.

Contribution

It provides an analytic stability criterion for slow rotation and numerically demonstrates a superradiant instability in rapidly rotating higher-dimensional AdS black holes.

Findings

No unstable modes for rotation parameter a < r_h^2/R

Instability appears for a > r_h^2/R with tiny growth rate

Superradiance likely causes the instability

Abstract

We study the stability of AdS black hole holes rotating in a single two plane for tensor-type gravitational perturbations in $D > 6$ space-time dimensions. First, by an analytic method, we show that there exists no unstable mode when the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$ is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical calculations of quasinormal modes, using the separability of the relevant perturbation equations, we show that an instability occurs for rapidly rotating black holes with $a>r_h^2/R$, although the growth rate is tiny (of order $10^{-12}$ of the inverse horizon radius). We give numerical evidences indicating that this instability is caused by superradiance.