Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

Abstract The phase transition and thermodynamic geometry of a 4-dimensional AdS topological charged black hole in de Rham, Gabadadze Tolley (dRGT) massive gravity have been studied. After introducing normalized scalar curvature, it is speculated that its value related to the interaction between underlying molecules if exist. We show there does exist crucial parameter given terms topology, charge, parameters hole, which characterizes properties hole. It found when positive, singlet large not for sufficient low temperature weak repulsive dominating small similar Reissner–Nordström hole; negative, an additional region describing holes also implies dominant interaction. These constitute distinguishable features dRGT from those as well Van der Waals fluid system.