Ruppeiner geometry, phase transitions and microstructures of black holes in massive gravity

Using the new normalized thermodynamic scalar curvature, we investigate the microstructures and phase transitions of black holes in massive gravity for horizons of various topologies. We find that the graviton mass enhances the repulsive interactions of small black holes and weakens the attractive interactions of large black holes, with possibility of new repulsive regions for microstructures in phase space. In addition, the repulsive interactions of small black hole are strong for spherical topology, followed by flat and hyperbolic topology; while, the attractive interactions of large black hole are strong for hyperbolic topology, followed by flat and weakest for spherical topology.