Renormalized vacuum polarization of rotating black holes

TL;DR

This paper introduces a novel method to compute the renormalized vacuum polarization and stress-energy tensor of quantum fields in rotating black hole spacetimes, overcoming previous technical challenges.

Contribution

The authors develop a general quasi-Euclidean technique to renormalize quantum fields on rotating black holes, applicable to physically relevant cases like Kerr black holes.

Findings

First general method for renormalized vacuum polarization in rotating black holes

Application to warped AdS3 black hole in topologically massive gravity

Enables computation of quantum stress-energy tensor in rotating black hole backgrounds

Abstract

Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2+1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization (and, more importantly, the renormalized stress-energy tensor), for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.