Black hole chemistry: thermodynamics with Lambda

TL;DR

This paper reviews the thermodynamics of black holes in extended phase space, where the cosmological constant acts as pressure, revealing new phase transitions and connections to chemical systems like Van der Waals fluids.

Contribution

It introduces a thermodynamic framework treating the cosmological constant as pressure, leading to new insights into black hole phase transitions and thermodynamic quantities.

Findings

Black holes exhibit Van der Waals-like phase transitions.

The thermodynamic volume satisfies a reverse isoperimetric inequality.

Black hole thermodynamics can be interpreted through chemical concepts.

Abstract

We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequality - an inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.