Thermodynamic Stability of Schwarzschild-de Sitter Black holes with R\'enyi entropy

TL;DR

This paper explores the thermodynamic stability of Schwarzschild-de Sitter black holes using Reny entropy, revealing conditions for stability and phase transitions that differ from classical approaches, with implications for quantum gravity.

Contribution

It introduces the treatment of the non-extensive parameter as a thermodynamic variable, extending the phase space and analyzing stability under Reny entropy.

Findings

Black holes are stable under Reny entropy but unstable with Gibbs-Boltzmann entropy.

Phase transitions from hot gas to stable black holes are identified.

Non-extensive effects may provide new insights into black hole thermodynamics.

Abstract

Even though, classically, a black holes is gravitational object, it can be treated as a thermodynamic object when quantum effect is taken into account. It is found that by using Gibbs-Boltzmann entropy, thermodynamic system associated Schwarzschild-de Sitter black hole is unstable while it is stable under description of R\'enyi entropy. According to R\'enyi entropy, the thermodynamic phase space needed to be extended. Specifically, the non-extensive parameter must be treated as a thermodynamic variable. In this work, we investigate the thermodynamic stability of Schwarzschild-de Sitter black hole with R\'enyi entropy by treating non-extensive parameter as chemical potential. We found that it is possible to obtain the stability of the black hole under the process with fixing pressure, temperature and number of particles. We also found that there exist the phase transitions from the hot gas to the stable black hole in such the process. Therefore, if such a black hole is possibly observed, the non-extensive effect of R\'enyi statistics may provide a physical insight beyond the standard approach to black hole thermodynamics.