Black Hole Quantum Vacuum Polarization in Higher Dimensions

Abstract

The goal of this paper is to extend to higher dimensionality the methods and computations of vacuum polarization effects in black hole spacetimes. We focus our attention on the case of five dimensional Schwarzschild-Tangherlini black holes, for which we adapt the general method initially developed by Candelas and later refined by Anderson and others. We make use of point splitting regularization and of the WKB approximation to extract the divergences occuring in the coincidence limit of the Green function and, after calculating the counter-terms using the Schwinger - De Witt expansion, we explicitly prove the cancellation of the divergences and the regularity of the vacuum polarization once counter-terms are added up. We finally handle numerically the renormalized expression of the vacuum polarization. As a check on the method we also prove the regularity of the vacuum polarization in the six dimensional case in the large mass limit.

14 pages, 2 Figures

References in corpus (6)

• Vacuum polarization in asymptotically anti-de Sitter black hole geometries
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions
• Renormalized stress tensor for massive fields in Kerr-Newman spacetime
• Vacuum Polarization of STU Black Holes and their Subtracted Geometry Limit
• Stress-energy tensor of the quantized massive fields in Schwarzschild-Tangherlini spacetimes. The back reaction

Cited by in corpus (3)

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