Classical instability of Kerr-AdS black holes and the issue of final state

TL;DR

This paper demonstrates that small Kerr-AdS black holes are unstable to both scalar and gravitational perturbations, analyzes the evolution of this instability, and identifies the endpoint state as a rotating Einstein universe boundary black hole.

Contribution

It provides the first detailed analysis of gravitational instability in small Kerr-AdS black holes and characterizes their final equilibrium state.

Findings

Small Kerr-AdS black holes are unstable to gravitational perturbations.

The endpoint state is a Kerr-AdS black hole with a rotating Einstein universe boundary.

The instability evolution leads to a slightly oblate black hole co-existing with outside radiation.

Abstract

It is now established that small Kerr-Anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its endpoint state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to co-exist in equilibrium with a certain amount of outside radiation.