# Quantum ergosphere and brick wall entropy

## TL;DR

This paper refines the brick wall model for black hole entropy by incorporating back-reaction effects, revealing a finite entropy contribution that aligns with the Bekenstein-Hawking formula, and introduces a quantum ergosphere concept.

## Contribution

It introduces a back-reaction modified metric and the concept of a quantum ergosphere, providing a finite entropy calculation consistent with established black hole thermodynamics.

## Key findings

- Back-reaction creates a quantum ergosphere that regularizes entropy calculations.
- Finite horizon entropy matches Bekenstein-Hawking entropy for Hawking flux luminosity.
- The model offers a more physically realistic approach to black hole entropy.

## Abstract

We revisit the "brick wall" model for black hole entropy taking into account back-reaction effects on the horizon structure. We do so by adopting an evaporating metric in the quasi-static approximation in which departures from the standard Schwarzschild metric are governed by a small luminosity factor. One of the effects of the back-reaction is to create an ergosphere-like region which naturally tames the usual divergence in the calculation of the partition function of the field. The black hole luminosity sets the width of such "quantum ergosphere". We find a finite horizon contribution to the entropy which, for the luminosity associated to the Hawking flux, agrees remarkably well with the Bekenstein-Hawking relation.