Renormalized Thermodynamic Entropy of Black Holes in Higher Dimensions

TL;DR

This paper investigates the divergent structures of scalar fields in higher-dimensional black holes and examines their impact on black hole entropy, revealing that matter contributions do not always correctly renormalize gravitational constants, especially in odd dimensions.

Contribution

It introduces a detailed analysis of matter field contributions to black hole entropy in higher dimensions using Pauli-Villars regularization, highlighting limitations in their renormalization effects.

Findings

Matter field contributions do not always correctly renormalize gravitational constants.

In odd dimensions, matter contributions lack terms proportional to the horizon area.

The regularization method reveals dimension-dependent differences in entropy contributions.

Abstract

We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstr\"{o}m black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon.