Geometrothermodynamics of black holes in Lorentz non-invariant massive gravity

Abstract

We analyze a static and spherically symmetric hairy black hole solution in non-invariant massive gravity. The formalism of geometrothermodynamics is used to describe the thermodynamic characteristics of this black hole in a Legendre invariant way. For a black hole in massive gravity, 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.