Thermodynamics of charged black holes with Maxwell and Born–Infeld fields in massive gravity theory

Abstract

In the framework of massive gravity theory which is coupled to the Maxwell and Born–Infeld electrodynamics, we review derivation of the exact four-dimensional black hole solutions by use of a static and spherically symmetric geometry. The exact solutions are asymptotically AdS and show two-horizon, one-horizon, extreme and black holes without horizon. The Maxwell and Born–Infeld black hole solutions are compatible in the limit of large nonlinearity parameter and, both reduce to the Reissner–Nordström black hole in the absence of massive gravitons. By reviewing thermodynamic and conserved quantities, and making use of a Smarr-type mass formula, we check validity of the thermodynamical first law for both of Maxwell and Born–infeld black holes. We investigate thermal stability of the black holes by use of the canonical ensemble and geometrical approaches, separately. By calculating the specific heats and Ricci scalars of alternative thermodynamic metrics, we compare the results of geometrothermodynamics with those of canonical ensemble method. Also, we perform a global stability analysis by use of the grand canonical ensemble and noting the Gibbs free energy of the Maxwell and Born–Infeld black holes.