Higher order WKB corrections to black hole entropy in brick wall formalism

TL;DR

This paper computes higher order WKB corrections to black hole entropy for quantum fields of arbitrary spin using the brick wall method, revealing logarithmic corrections to the Bekenstein-Hawking entropy.

Contribution

It extends the brick wall formalism to include higher order WKB corrections for arbitrary spin fields on black hole backgrounds, providing new insights into entropy corrections.

Findings

Logarithmic correction to black hole entropy proportional to horizon area

Application to Schwarzschild and Schwarzschild-AdS black holes

Generalization to arbitrary spin fields

Abstract

We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein-Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild-AdS black holes and discuss our results.