Renormalized vacuum polarization on rotating warped AdS3 black holes

TL;DR

This paper calculates the renormalized vacuum polarization of a scalar field around rotating warped AdS3 black holes, introducing a numerical method that could extend to more complex spacetimes like Kerr.

Contribution

It presents a new numerical approach for computing vacuum polarization in rotating black holes without analytic continuation in angular momentum.

Findings

Numerical method successfully applied to warped AdS3 black holes.

Method avoids analytic continuation in angular momentum.

Results suggest applicability to Kerr spacetime in 4D.

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.