Abstract: (2+1)-dimensional gravity allows us to study aspects of classical and quantum gravity in a simpler technical setting which retains much of the conceptual complexity of the standard (3+1)-dimensional gravity. However, pure Einstein gravity lacks propagating degrees of freedom in 2+1 dimensions. Topologically Massive Gravity is a modification of GR which adds a gravitational Chern-Simons term to the Einstein-Hilbert action and which includes propagating degrees of freedom. Besides the famous BTZ black hole solution, this theory has a whole new class of black hole solutions -- the warped AdS3 black holes -- which can be viewed as deformed BTZ solutions but which, counterintuitively, are not asymptotically AdS -- they are actually (almost) asymptotically flat! In this talk, I will describe the classical features of this interesting set of solutions. First, I will show that, in contrast with the BTZ solution, classical superradiance of a scalar field on the background of a warped AdS3 black hole is always present. Despite this fact, I then show that the black hole is classically stable (at a linear level), namely there are no superradiant instabilities, even if it 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, which is classically unstable due to superradiant instabilities.
This work has been published in Phys. Rev. D 87, 124013 (2013).