Geometric description of black hole thermodynamics with homogeneous fundamental equation

Abstract

We investigate the Geometrothermodynamics of the 2-dimensional submanifold E corresponding the space of thermodynamic equilibrium states for a static and spherically symmetric hairy to black hole solution in Lorentz non-invariant massive gravity. We show that it is possible to consider a fundamental thermodynamic function as a homogeneous function of degree 1 in the extensive variables, as classical thermodynamics demand, in order to be consistent with the physical meaning of the intensive variables. The geometry of the space of equilibrium states is computed showing that it contains information about the thermodynamic interaction, critical points, and phase transitions structure.