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.

中文翻译：

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大质量黑洞的鲁佩纳几何、相变和微观结构

使用新的归一化热力学标量曲率，我们研究了各种拓扑视界的大质量黑洞的微观结构和相变。我们发现，引力子质量增强了小黑洞的排斥作用，削弱了大黑洞的吸引力作用，相空间中的微结构有可能出现新的排斥区域。此外，小黑洞的排斥作用在球形拓扑中强，其次是平面和双曲拓扑；而大黑洞的引力相互作用对于双曲拓扑来说是强的，其次是平坦的，对于球形拓扑来说是最弱的。