Divergences problem in black hole brick-wall model

TL;DR

This paper reviews the divergence issues in the black hole brick-wall model's thermodynamical calculations and proposes a solution based on the zeroth law of black hole mechanics.

Contribution

It identifies divergence problems in the brick-wall model and proposes a novel solution aligned with black hole thermodynamics principles.

Findings

Divergences occur in entropy, energy, and heat capacity calculations.

Matching entanglement entropy with Bekenstein-Hawking entropy leads to problematic results.

A proposed solution addresses divergence issues using the zeroth law of black hole mechanics.

Abstract

In this work we review, in the framework of the so-called brick wall model, the divergence problem arising in the one loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. Particularly we find that, if one imposes that entanglement entropy is equal to the Bekenstein-Hawking one, the model gives problematic results. Then a proposal of solution to the divergence problem is made following the zeroth law of black hole mechanics.