The double doors of the horizon

TL;DR

This paper explores the nature of black hole entropy, proposing that classical gravity may explain the large entropy increase, and discusses the implications for understanding phase space volume in black hole thermodynamics.

Contribution

It offers a hypothesis that classical gravity influences the large entropy of black holes, connecting thermodynamics and quantum gravity effects.

Findings

Large black hole entropy may be explained by classical gravity effects.

Quantum gravity may set a limit to entropy increase.

Discussion of existing literature on black hole thermodynamics.

Abstract

In statistical mechanics entropy is a measure of disorder obeying Boltzmann's formula $S=\log{\cal N}$, where ${\cal N}$ is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy Bekenstein-Hawking $S_{BH}$. It is well known that $S_{BH}$ is very large for astrophysical black holes, much larger than any collection of material objects that could have given rise to the black hole. If $S_{BH}$ is an entropy the question is thus what is the corresponding ${\cal N}$, and how come this very large phase space volume is only opened up to the universe by a gravitational collapse, which from another perspective looks like a massive loss of possibilities. I advance a hypothesis that the very large increase in entropy can perhaps be understood as an effect of classical gravity, which eventually bottoms out when quantum gravity comes into play. I compare and discuss a selection of the very rich literature around these questions.