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We demonstrate that the warped AdS3 black hole solutions of TopologicallyMassive Gravity are classically stable against massive scalar fieldperturbations by analysing the quasinormal and bound state modes of the scalarfield. In particular, it is found that although classical superradiance ispresent it does not give rise to superradiant instabilities. The stability isshown to persist even when the black hole is enclosed by a stationary mirrorwith Dirichlet boundary conditions. This is a surprising result in view of thesimilarity between the causal structure of the warped AdS3 black hole and theKerr spacetime in 3+1 dimensions. This work provides the foundations for thestudy of quantum field theory in this spacetime.

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