Effective thermodynamical system of Schwarzschild-de Sitter black holes from R\'{e}nyi statistics

TL;DR

This paper explores how Rényi statistics can stabilize Schwarzschild-de Sitter black holes thermodynamically by incorporating non-extensive effects, revealing new stability conditions and phase transition behaviors.

Contribution

It introduces an effective thermodynamic framework using Rényi statistics to stabilize Schwarzschild-de Sitter black holes, highlighting the role of non-extensivity in black hole thermodynamics.

Findings

Non-extensivity stabilizes black holes thermodynamically.

Effective temperature is always smaller than horizon temperature.

Only zeroth-order phase transition occurs in the effective system.

Abstract

It has been known that the Schwarzschild-de Sitter (Sch-dS) black hole may not be in thermal equilibrium and also be found to be thermodynamically unstable in the standard black hole thermodynamics. In the present work, we investigate the possibility to realize the thermodynamical stability of the Sch-dS black hole as an effective system by using the R\'{e}nyi statistics, which includes the non-extensive nature of black holes. Our results indicate that the non-extensivity allows the black hole to be thermodynamically stable which gives rise to the lower bound on the non-extensive parameter. By comparing the results to ones in the separated system approach, we find that the effective temperature is always smaller than the black hole horizon temperature and the thermodynamically stable black hole in effective approach is always larger than one in separated approach at a certain temperature. There exists only the zeroth-order phase transition from the the hot gas phase to the black hole phase for the effective system while it is possible to have the transition of both the zeroth order and the first order for the separated system.