Sub-leading contributions to the black hole entropy in the brick wall approach

TL;DR

This paper calculates higher-order quantum corrections to black hole entropy using the brick wall method, revealing dimension-dependent modifications to the Bekenstein-Hawking entropy formula.

Contribution

It extends the brick wall approach to sixth order in ar, providing explicit forms of entropy corrections in various spacetime dimensions.

Findings

Corrections in 4D are of the form A^n log A.

In 6D, corrections include A^m and A^n log A terms.

Results align with other approaches, highlighting universal features.

Abstract

[Abridged] We compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in \hbar) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form (A^n \log A), while, in six dimensions, the corrections behave as (A^m + A^n \log A), where A denotes the area of the black hole event horizon, and (m, n) < 1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.