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 deformation of GR which includes propagating degrees of freedom. Besides the famous BTZ black hole solution, this theory has a whole new class of rotating 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! This gives us a (2+1)-dimensional black hole which closely resembles the Kerr black hole in 3+1 dimensions.

In this talk, I will describe the issues of mode stability and quantum field theory of this interesting set of solutions. First, I will show that, in contrast with the BTZ solution, classical superradiance of a massive 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 to scalar perturbations, 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. Finally, I will report on current progress on the computation of the renormalised stress-energy tensor of a scalar field in the Hartle-Hawking vacuum using the Hadamard renormalisation technique. When finished, this work will provide the first calculation of this kind for a rotating black hole with asymptotics which resemble asymptotically flat spacetimes.

Part of this work has been published in Phys. Rev. D 87 , 124013 (2013).