VACUUM POLARIZATION OF MASSIVE FIELDS IN THE SPACETIME OF THE HIGHER-DIMENSIONAL BLACK HOLES

Using the Schwinger-DeWitt expansion, we construct and study the approximate vacuum polarization, <phi(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 obtained when the Compton length associated with the quantized field is much less than the characteristic radius of the curvature of the background geometry and the nonlocal contribution to the result ignored. 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.