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The thermodynamics of the Kerr-AdS black hole is reformulated within thecontext of the formalism of geometrothermodynamics (GTD) and the cosmologicalconstant is considered as a new thermodynamical parameter. We conclude that themass of the black hole corresponds to the total enthalpy of this system.Choosing appropriately the metric in the equilibrium states manifold, we studythe phase transitions as a divergence of the thermodynamical curvature scalar.This approach reproduces the Hawking-Page transition and shows that consideringthe cosmological constant as a thermodynamical parameter does not contributewith new phase transitions.

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