Geometric Thermodynamics of Schwarzschild-AdS black hole with a Cosmological Constant as State Variable

The thermodynamics of the Schwarzschild-AdS black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Different choices of the metric in the equilibrium states manifold are used in order to reproduce the Hawking-Page phase transition as a divergence of the thermodynamical curvature scalar. We show that the enthalpy and total energy representations of GTD does not reproduce the transition while the entropy rep- resentation gives the expected behavior.