Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

Phuwadon Chunaksorn; Ekapong Hirunsirisawat; Ratchaphat Nakarachinda; Lunchakorn Tannukij; Pitayuth Wongjun

doi:10.1140/epjc/s10052-022-11110-5

2022 Impact factor 4.4

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 1174
https://doi.org/10.1140/epjc/s10052-022-11110-5

Regular Article - Theoretical Physics

Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

Phuwadon Chunaksorn¹^,2, Ekapong Hirunsirisawat³^,4, Ratchaphat Nakarachinda¹, Lunchakorn Tannukij⁵ and Pitayuth Wongjun¹^,2^e

¹ The Institute for Fundamental Study, Naresuan University, 65000, Phitsanulok, Thailand
² Thailand Center of Excellence in Physics, Ministry of Higher Education, Science, Research and Innovation, 328 Si Ayutthaya Road, 10400, Bangkok, Thailand
³ Quantum Computing and Theory Research Centre (QX), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Pracha Uthit Road, 10140, Bangkok, Thailand
⁴ Learning Institute, King Mongkut’s University of Technology Thonburi (KMUTT), Pracha Uthit Road, 10140, Bangkok, Thailand
⁵ Department of Physics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, 1 Chalong Krung 1 Alley, Lat Krabang, 10520, Bangkok, Thailand

^e pitbaa@gmail.com

Received: 21 September 2022
Accepted: 5 December 2022
Published online: 28 December 2022

Abstract

The thermodynamic properties of the de Rham–Gabadadze–Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using Rényi 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 Rényi statistics to analyze the thermodynamic 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.

© The Author(s) 2022

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