Vacuum Polarization of Massive Fields in the Spacetime of the Higher-dimensional Black Holes

Abstract

We construct and study the vacuum polarization, φ 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 ≤ D ≤ 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.