Quantum scalar field in D-dimensional static black hole space-times

Abstract

An Euclidean approach for investigating quantum aspects of a scalar field living on a class of D-dimensional static black hole space-times, including the extremal ones, is reviewed. The method makes use of a near horizon approximation of the metric and $\zeta$-function formalism for evaluating the partition function and the expectation value of the field fluctuations $<{\varphi }^2(x)>$. After a review of the non-extreme black hole case, the extreme one is considered in some details. In this case, there is no conical singularity, but the finite imaginary time compactification introduces a cusp singularity. It is found that the $\zeta$-function regularized partition function can be defined, and the quantum fluctuations are finite on the horizon, as soon as the cusp singularity is absent, and the corresponding temperature is T=0.

9 pages, LaTex

References in corpus (5)

• Topological Black Holes in Anti-de Sitter Space
• Black holes with unusual topology
• Local $\zeta$-function techniques vs point-splitting procedure: a few rigorous results
• zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times
• Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

Cited by in corpus (5)

• Hawking Radiation as Tunneling for Extremal and Rotating Black Holes
• Fluctuations of quantum fields via zeta function regularization
• On the Dimensional Reduction Procedure
• Quantum detectors in generic non flat FLRW space-times
• Vacuum fluctuation of conformally coupled scalar field in FLRW space-times