Black holes and Boyle's law -- the thermodynamics of the cosmological constant

TL;DR

This paper reviews the emerging thermodynamic framework where the cosmological constant is treated as a pressure, revealing complex structures in black hole thermodynamics and introducing the concept of thermodynamic volume.

Contribution

It introduces and discusses the interpretation of the cosmological constant as a thermodynamic pressure and explores the resulting rich thermodynamic structure of black holes.

Findings

The cosmological constant can be treated as a thermodynamic pressure.

A thermodynamic volume conjugate to pressure is defined for black holes.

This approach uncovers new thermodynamic phenomena in black hole physics.

Abstract

When the cosmological constant, $\Lambda$, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret $\Lambda$ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.