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

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 HawkingPage 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.

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

“…Indeed, after some careful analysis of the present model, one can show that the H λ=0 (S BH ) function of the Bekenstein-Hawking entropy in the system is always the mass-energy parameter of the black hole up to some constant factor, so the new entropy function can only result a constant temperature, no matter what complicated black hole spacetime is considered. Comparing these findings with our previous results on the problem by using the parametric Tsallis-Rényi approach [24,25,33], we conclude that the present non-parametric approach to black hole thermodynamics based on the Bekenstein-Hawking entropy nonadditivity is most likely an unrealistic one. Based on this conclusion, it is more reasonable to further study the parametric λ = 0 case, where the zeroth law-compatible temperature function of the system is not independent of the black hole mass.…”

“…To extend the above studies on the Schwarzschild-Rényi model, we have also examined the thermodynamic and stability properties of Kerr black holes within the Tsallis-Rényi approach [33]. We analyzed the thermodynamic stability of the problem in both the microcanonical and canonical ensembles, and found a stability change in the latter case.…”

Non-extensive statistical mechanics and black hole entropy from quantum geometry

“…It will be interesting to shed some light on the problem of black hole entropy calculation from LQG using NESM for γ = ±i if we can ever solve the above issues. Apart from this, from a broader perspective, this work establishes a key link between the microscopic theory of black holes in LQG and the phenomenology associated with the application of NESM to black hole thermodynamics problems [25][26][27]. We hope that our results will lead to further innovative works in this direction.…”

Embolic aspects of black hole entropy

“…This has been a topic of continuous interest for the last few decades [27,28]. Another direction of potential interest is to investigate the microscopic origin of the black hole entropy and examine, in particular, whether it is of the usual Boltzmann/Gibbs/Shannon or of another, maybe power-law, functional form [29,30,31,32,33].…”