Geometrothermodynamics of black holes in Lorentz non-invariant massive   gravity
  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. 
Alberto Sanchez
gr-qc hep-th math-ph math.MP