We demonstrate that the warped ${\mathrm{AdS}}_3$ black hole solutions of topologically massive gravity are classically stable against massive scalar field perturbations by analyzing 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 ${\mathrm{AdS}}_3$ 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.

• Received 23 April 2013

DOI:https://doi.org/10.1103/PhysRevD.87.124013