Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity

TL;DR

This paper explores how massive gravity influences black hole microstructures and phase transitions using thermodynamic scalar curvature, revealing topology-dependent interaction behaviors and the impact of graviton mass.

Contribution

It introduces a normalized thermodynamic scalar curvature to analyze black hole microstructures in massive gravity, highlighting the effects of graviton mass on interactions and phase behavior.

Findings

Graviton mass enhances repulsive interactions in small black holes.

Large black holes exhibit weakened attractive interactions due to graviton mass.

Topology affects interaction strength: spherical favors strong repulsion, hyperbolic favors attraction.

Abstract

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 possiblity 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.