One-loop Quantum Holography for Higher Dimensional Black Holes

TL;DR

This paper computes one-loop quantum corrections to black hole free energy in higher dimensions, revealing holographic area law behavior and emphasizing the special role of asymptotically AdS black holes for microscopic entropy interpretation.

Contribution

It introduces a conformal transformation method to evaluate quantum corrections in higher-dimensional black holes, highlighting the holographic nature of quantum effects and the unique status of AdS black holes.

Findings

Quantum corrections follow the area law holographically.

Horizon divergences are regularized using the Planck length.

Only AdS black holes allow a microscopic entropy interpretation at quantum level.

Abstract

The one-loop quantum corrections to the free energy associated with scalar field in a higher dimensional static curved space-time is investigated making use of the conformal transformation method. For a space-time with bifurcate horizon, horizon divergences are accounted for choosing the Planck length as natural cutoff. The leading term in the high temperature quantum correction satifies holographically the "area law", like the tree level Bekenstein-Hawking term. Furthermore it is stressed that only for the asymptotically AdS black holes one may have a microscopic interpretation of the entropy also at quantum level.