Extended phase space thermodynamics of Bardeen black hole in massive gravity

Abstract

We present an exact solution of Bardeen AdS black hole in massive gravity theory by taking into account the massive gravity parameter m and study its thermodynamic properties such as temperature, entropy and heat capacity at constant pressure. We also study the critical behaviour of Bardeen AdS massive black holes by taking the cosmological constant $$\Lambda $$ as the thermodynamic pressure, and it is shown that thermodynamic volume is independent of the massive gravity parameter m. In addition to these, we investigate the dependence of critical parameters on the massive gravity parameter (m) and magnetic monopole charge (e). It is observed that the critical exponents (critical temperature and critical pressure) increase with massive gravity parameter but decrease in the presence of magnetic monopole charge. Also the numerical value of ratio $$P_\mathrm{c}r_\mathrm{c}/T_\mathrm{c}$$ increases with increase in the values of the parameters m and e.