Quantum Corrections to Entropy of Charged Dilatonic Black Holes in Arbitrary Dimensions

TL;DR

This paper calculates quantum corrections to the entropy of charged dilatonic black holes across arbitrary dimensions, revealing that the leading divergence is proportional to the horizon area and independent of other black hole properties.

Contribution

It provides a detailed analysis of quantum entropy corrections using the brick wall model and WKB method, extending understanding to arbitrary-dimensional dilatonic black holes.

Findings

Leading divergence in entropy is proportional to horizon area.

Quantum corrections are independent of black hole properties.

Results are consistent with known subleading divergences for N=3.

Abstract

The quantum contribution of a scalar field to entropy of a dilatonic black hole is calculated in the brick wall model by the WKB method and analyzed by a high-temperature expansion. If the cutoff distance from the horizon approaches zero, the leading divergent piece of entropy turns out to be proportional to the "area" of the horizon surface (which has (N-1)-dimensional extension in (N+1)-dimensional space-time) and independent of other properties of black holes even in the case of general dilaton coupling. There is also qualitative argument with the known result of subleading divergence for N=3.