Fine micro-thermal structures for Reissner-Nordström black hole * * The financial supports from National Natural Science Foundation of China (11947208, 11947301, 11605137), China Postdoctoral Science Foundation (2020M673460), Major Basic Research Program of Natural Science of Shaanxi Province (2017KCT-12), Scientific Research Program Funded by Shaanxi Provincial Education Department (18JK0771) are gratefully acknowledged

Abstract

We solve the condundrum on whether the molecules of the Reissner-Nordström black hole interact through the Ruppeiner thermodynamic geometry, basing our study on the concept of the black hole molecule proposed in [Phys. Rev. Lett. 115 (2015) 111302] and choosing the appropriate extensive variables. Our results show that the Reissner-Nordström black hole is indeed an interaction system that may be dominated by repulsive interaction. More importantly, with the help of a novel quantity, namely the thermal-charge density, we describe the fine micro-thermal structures of the Reissner-Nordström black hole in detail. Three different phases are presented, namely the free, interactive, and balanced phases. The thermal-charge density plays a role similar to the order parameter, and the back hole undergoes a new phase transition between the free phase and interactive phase. The competition between the free phase and interactive phase exists, which leads to extreme behavior of the temperature of the Reissner-Nordström black hole. For the extreme Reissner-Nordström black hole, the entire system is completely in the interactive phase. More importantly, we provide the thermodynamic micro-mechanism for the formation of the naked singularity of the Reissner-Nordström black hole.