Quantum vacuum polarization around a Reissner-Nordstr\"om black hole in five dimensions

TL;DR

This paper applies WKB approximation to analyze quantum vacuum polarization of a massive scalar field around a five-dimensional charged black hole, extending previous uncharged black hole results.

Contribution

It extends prior work by including electric charge in the analysis of quantum vacuum polarization effects in higher-dimensional black holes.

Findings

Explicit isolation and cancellation of divergences with Schwinger-De Witt counter-terms.

Finite vacuum polarization results evaluated for various black hole and scalar field parameters.

Extension of previous uncharged black hole results to charged black holes in five dimensions.

Abstract

WKB approximation methods are applied to the case of a massive scalar field around a 5-dimensional Reissner-Nordstr\"om black hole. The divergences are explicitly isolated and the cancellation against the Schwinger-De Witt counter-terms proven. The resulting finite quantity is evaluated for different values of the free parameters, namely the black hole mass and charge, and the scalar field mass. We thus extend our previous results on quantum vacuum polarization effects for uncharged asymptotically flat higher dimensional black holes to electrically charged black holes.