(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, in 2+1 dimensions pure Einstein gravity is a topological theory. By adding a gravitational Chern-Simons term to the action, one obtains Topologically Massive Gravity, which 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 Kerr black hole, the warped AdS3 black hole is classically stable to massive scalar field perturbations, by analysing its mode stability. Finally, I will report on current progress on the Hadamard renormalisation of the stress-energy tensor of a scalar field in the Hartle-Hawking vacuum. 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).