Rényi entropy and the thermodynamic stability of black holes

Abstract

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking-Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

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.…”

“…Recently, based on the above formal logarithm approach to the nonextensive problem of black hole thermodynamics, we investigated the thermodynamic [24] and stability [25] properties of the Schwarzschild solution. In the analysis of [24], we regarded the Bekenstein-Hawking entropy of black hole event horizons as a nonextensive Tsallis entropy, which for small energies and for small parameter values (λ = 1 − q) was assumed to follow the nonadditive Tsallis composition law (4).…”

“…In [25], we also investigated the thermodynamic stability of the problem. In the standard Boltzmann picture, Schwarzschild black holes seem to be thermodynamically unstable in the canonical treatment because their heat capacity is always negative.…”

“…In [25], we first investigated the question of a pure, isolated black hole in the microcanonical ensemble. We showed that these configurations are stable against spherically symmetric perturbations, just like in the classical picture.…”

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

“…By considering the Rényi model in the black hole problem, we also investigated the thermodynamic stability question of Schwarzschild black holes [54]. First we considered the question of pure, isolated black holes in the microcanonical approach, and showed that these configurations are stable against spherically symmetric perturbations, just like in the Boltzmann picture.…”