Effective thermodynamical system of Schwarzschild-de Sitter black holes from Rényi statistics

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 Rényi 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 nonextensive 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.

Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach

“…The role of nonextensive parameter λ to stabilize the black holes is in a similar fashion as the gravitational potential with negative cosmological constant Λ in AdS space. Moreover, the nonextensive effect can stabilize the Schwarzschild black hole in a de Sitter spacetime of the positive cosmological constant as well [23,24].…”