Renormalized vacuum polarization on rotating warped AdS3 black holes

Abstract

We compute the renormalized vacuum polarization of a massive scalar field in the Hartle-Hawking state on (2+1)-dimensional rotating, spacelike stretched black hole solutions to Topologically Massive Gravity, surrounded by a Dirichlet mirror that makes the state well defined. The Feynman propagator is written as a mode sum on the complex Riemannian section of the spacetime, and a Hadamard renormalization procedure is implemented by matching to a mode sum on the complex Riemannian section of a rotating Minkowski spacetime. No analytic continuation in the angular momentum parameter is invoked. Selected numerical results are given, demonstrating the numerical efficacy of the method. We anticipate that this method can be extended to wider classes of rotating black hole spacetimes, in particular to the Kerr spacetime in four dimensions.

25 pages, 2 figures. v2: minor typos corrections, published version

References in corpus (5)

• Warped AdS_3 Black Holes
• Three-dimensional Chern-Simons black holes
• From accelerating and Poincaré coordinates to black holes in spacelike warped AdS${}_3$, and back
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• Renormalized stress tensor for massive fields in Kerr-Newman spacetime

Cited by in corpus (4)

• Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
• Vacuum polarization on topological black holes with Robin boundary conditions
• Renormalized vacuum polarization of rotating black holes
• Vacuum fluctuations and the renormalized stress-energy tensor on a cone with arbitrary boundary conditions