Vacuum polarization of massive fields in the spacetime of the higher-dimensional black holes

TL;DR

This paper analyzes the vacuum polarization of massive scalar fields in higher-dimensional black hole spacetimes, providing explicit formulas and exploring the relation between stress-energy trace and vacuum polarization.

Contribution

It offers the first explicit analytic expressions for vacuum polarization in dimensions 4 to 7 for higher-dimensional black holes, including charged and extremal cases.

Findings

Explicit formulas for vacuum polarization in 4-7 dimensions.

Relation between stress-energy trace and vacuum polarization for conformally coupled fields.

Analysis of extremal and ultraextremal black hole configurations.

Abstract

We construct and study the vacuum polarization, $\langle \phi^{2}\rangle_{D},$ of the quantized massive scalar field with a general curvature coupling parameter in higher-dimensional static and spherically-symmetric black hole spacetimes, with a special emphasis put on the electrically charged Tangherlini solutions and the extremal and ultraextremal configurations. For $4 \leq D \leq 7$ the explicit analytic expressions for the vacuum polarization are given. For the conformally coupled fields the relation between the trace of the stress-energy tensor and the vacuum polarization is examined, which requires knowledge of the higher-order terms in the Schwinger-DeWitt expansion.