The entropy of Hawking radiation and the generalized second law

TL;DR

This paper derives an approximate entropy expression for Hawking radiation in equilibrium with a black hole, highlighting potential issues with the generalized second law of thermodynamics.

Contribution

It provides a new approximate formula for Hawking radiation entropy and discusses conditions where the generalized second law may not hold.

Findings

Bekenstein entropy bound is satisfied

Generalized second law may not always be guaranteed

Discussion on the origin of this unexpected result

Abstract

We derive an approximate expression for the entropy of Hawking radiation filling a spherical box in stable thermodynamic equilibrium with the Schwarzschild black hole that produced the said radiation. The Bekenstein entropy bound is satisfied but the generalized second law might not be always guaranteed. We briefly discuss the possible origin of this unexpected result.