The cosmological constant and the black hole equation of state

TL;DR

This paper explores black hole thermodynamics with a negative cosmological constant, treating it as pressure, and investigates quantum corrections to their equations of state, revealing new insights into their thermodynamic behavior.

Contribution

It introduces a framework where the cosmological constant acts as pressure, redefining black hole mass as enthalpy and analyzing quantum effects on black hole thermodynamics.

Findings

Black hole mass identified with enthalpy instead of internal energy.

Thermodynamic properties derived with the cosmological constant as pressure.

Quantum corrections to BTZ black hole's enthalpy and equation of state studied.

Abstract

The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume. The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.