Vacuum polarization on topological black holes

TL;DR

This paper studies quantum effects, specifically vacuum polarization, around topological black holes in anti-de Sitter space, extending regularization methods to nonspherical horizons and comparing results with spherical cases.

Contribution

It extends mode-sum regularization for vacuum polarization to topological black holes with nonspherical horizons in anti-de Sitter space.

Findings

Calculated vacuum polarization for a massless, conformally-coupled scalar field.

Compared vacuum polarization results between topological and spherical black holes.

Demonstrated the applicability of the regularization method to nonspherical horizon topologies.

Abstract

We investigate quantum effects on topological black hole space-times within the framework of quantum field theory on curved space-times. Considering a quantum scalar field, we extend a recent mode-sum regularization prescription for the computation of the renormalized vacuum polarization to asymptotically anti-de Sitter black holes with nonspherical event horizon topology. In particular, we calculate the vacuum polarization for a massless, conformally-coupled scalar field on a four-dimensional topological Schwarzschild-anti-de Sitter black hole background, comparing our results with those for a spherically-symmetric black hole.