Thermodynamics of Asymptotically de-Sitter Black Hole in dRGT Massive Gravity from R\'{e}nyi entropy

TL;DR

This paper explores the thermodynamics of asymptotically de Sitter black holes in dRGT massive gravity using Rènyi entropy, revealing conditions for stability and differences from standard approaches.

Contribution

It introduces Rènyi entropy into the thermodynamic analysis of dRGT black holes, demonstrating the possibility of stable configurations with positive pressure and volume.

Findings

Stable black hole configurations with positive pressure and volume are possible.

Bounds on the nonextensive parameter for thermodynamic stability are established.

Differences in temperature profiles and phase transitions between approaches are identified.

Abstract

The thermodynamic properties of the de Rham-Gabadadze-Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using R\'enyi entropy. It has been found that the black hole with asymptotically dS spacetime described by the standard Gibbs-Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to two thermodynamic systems with different temperatures, leading to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black hole, we use the alternative R\'enyi statistics to analyze the thermodynamics properties in both the separated system approach and the effective system approach. Interestingly, we found that it is possible concurrently obtain positive pressure and volume for the dRGT black hole while it is not for the Schwarzschild-de Sitter (Sch-dS) black hole. Furthermore, the bounds on the nonextensive parameter for which the black hole being thermodynamically stable are determined. In addition, the key differences between the systems described by different approaches, e.g., temperature profiles and types of the Hawking-Page phase transition are pointed out.