Extended phase space thermodynamics for Bardeen black holes in massive gravity

TL;DR

This paper investigates the thermodynamics and phase transitions of Bardeen black holes in massive gravity, analyzing how parameters like magnetic charge and mass influence critical behavior and thermodynamic properties.

Contribution

It provides an exact solution for Bardeen black holes in massive gravity and explores their thermodynamic phase structure with novel insights into parameter effects.

Findings

Critical values of pressure and temperature are identified.

Thermodynamic volume is independent of the mass parameter.

Magnetic charge and mass parameter have opposite effects on phase transition.

Abstract

This paper presents an exact solution of Bardeen black hole in presence of massive gravity, which is characterized by the additional parameter $m$. Here, we focus on $4D$ Bardeen AdS massive black hole solutions as example to discuss the thermodynamical properties such as temperature, entropy and specific heat at constant pressure. We also study the critical behaviour of Bardeen AdS massive black holes by considering the cosmological constant $\Lambda$ as thermodynamical variable (pressure) as well as the parameter associated with the nonlinear electrodynamics. We calculate the critical value of pressure and temperature and study the effect of magnetic charge $e$ and mass parameter $m$. It is seen that the thermodynamical volume are the independent of mass parameter $m$. The critical values are the one in which phase transition takes place and the nature of mass parameter $m$ and magnetic charge $e$ are opposite to each other. The critical temperature and pressure were highly sensitive for these parameters.