Eur. Phys. J. C (2017) 77: 892
https://doi.org/10.1140/epjc/s10052-017-5453-x

Regular Article - Theoretical Physics

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

¹ Multidisciplinary Center for Astrophysics and Department of Physics, Instituto Superior Técnico, University of Lisbon, Avenida Rovisco Pais 1, 1049-001, Lisboa, Portugal
² HAS Wigner Research Centre for Physics, P.O. Box 49, Budapest, 1525, Hungary
³ Laboratory of Physics, College of Science and Technology, Nihon University, 274-8501, Narashinodai, Funabashi, Chiba, Japan

^* e-mail: viktor.czinner@tecnico.ulisboa.pt

Received: 13 June 2017
Accepted: 8 December 2017
Published online: 20 December 2017

Abstract

Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking–Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann–AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.