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

Understand

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.