Geometrothermodynamics of black holes

Understand

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics.

• This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations.
• Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold's and Ruppeiner's thermodynamic metrics for black holes.
• For the Reissner-Nordstr\"om black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions.