  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.
