Thermodynamics and geometrothermodynamics of Born-Infeld black holes with cosmological constant

In this paper, we investigate a class of spherically symmetric Born-Infeld black holes which contains the mass, electric charge, Born-Infeld parameter and the cosmological constant as physical parameters. We show that for the mass to be an extensive thermodynamic variable, it is necessary to consider the cosmological constant and the Born-Infeld parameter as thermodynamic variables as well. We analyze the properties of such a thermodynamic system, explore the range of values where the system is thermodynamically well-defined, and the phase transition structure. In addition, we show that the equilibrium manifold in the context of geometrothermodynamics reproduces correctly the thermodynamic properties of this black hole class.