P-V criticality in AdS black holes of massive gravity

TL;DR

This paper explores the thermodynamic phase transitions of AdS black holes in massive gravity, revealing Van der Waals-like behavior and critical phenomena similar to standard fluids.

Contribution

It provides a detailed analysis of phase transitions and critical exponents of black holes in massive gravity, extending the understanding of black hole thermodynamics in modified gravity theories.

Findings

Black holes exhibit Van der Waals-like phase transitions.

Critical exponents match those of Van der Waals fluids.

Thermodynamical stability analyzed in detail.

Abstract

In this paper we have studied the extended phase space thermodynamics in the canonical ensemble of black holes in massive gravity in AdS space. The black holes considered here belong to a theory of massive gravity where the graviton gain a mass due to Lorentz symmetry breaking. We have computed various thermodynamical quantities such as temperature, pressure, Gibbs free energy and specific heat capacity. The local and the global thermodynamical stability of the black holes are studied in detail. For a specific value of the parameter in the theory, the black holes undergo a first order phase transition similar to the Van der Waals phase transitions between gas and liquid under constant temperature. This transition is between the small and the large black hole. The critical exponents are computed at the critical values and shown to be the same as for the Van der Waals critical exponents.