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

Abstract

We construct and study the vacuum polarization, $⟨{\varphi }^2{⟩}_D,$ 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 $4\le D\le 7$ 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.

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