Stability of warped AdS3 black holes in Topologically Massive Gravity under scalar perturbations

TL;DR

This paper proves that warped AdS3 black holes in Topologically Massive Gravity are classically stable against scalar perturbations, even with superradiance and boundary conditions, supporting further quantum field theory studies.

Contribution

It demonstrates the classical stability of warped AdS3 black holes under scalar perturbations, including superradiance effects and boundary conditions, which was previously uncertain.

Findings

Black holes are stable against scalar perturbations.

Superradiance does not lead to instabilities.

Stability persists with boundary conditions.

Abstract

We demonstrate that the warped AdS3 black hole solutions of Topologically Massive Gravity are classically stable against massive scalar field perturbations by analysing the quasinormal and bound state modes of the scalar field. In particular, it is found that although classical superradiance is present it does not give rise to superradiant instabilities. The stability is shown to persist even when the black hole is enclosed by a stationary mirror with Dirichlet boundary conditions. This is a surprising result in view of the similarity between the causal structure of the warped AdS3 black hole and the Kerr spacetime in 3+1 dimensions. This work provides the foundations for the study of quantum field theory in this spacetime.