Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

TL;DR

This paper investigates the thermodynamic phase transitions of hairy black holes in massive gravity and charged AdS black holes in extended phase space, revealing Van der Waals-like behavior and second order phase transitions.

Contribution

It introduces the thermodynamic analysis of hairy black holes in massive gravity and explores phase transitions in charged AdS black holes with extended phase space variables.

Findings

Hairy black holes exhibit Van der Waals-like phase transitions.

Charged AdS black holes show second order phase transitions for all electric potentials.

Thermodynamic behavior is studied with fixed temperature and extended variables.

Abstract

We study the thermodynamic behavior of static and spherically symmetric hairy black holes in massive gravity. In this case, the black hole is surrounded in a spherical cavity with a fixed temperature on the surface. It is observed that these black holes have a phase transition similar to the liquid-gas phase transition of a Van der Waals fluid. Also, by treating the cosmological constant $\Lambda$ as a thermodynamic pressure $P$, we study the thermodynamic behavior of charged anti-de Sitter black holes in an ensemble with a pressure of $P$ and an electric potential $\Phi$ as the natural variables. A second order phase transition is observed to take place for all the values of the electric potential $\Phi$.