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.
Highlights
AdS ones, and in the standard black hole thermodynamic picture [6,7,8,9], they mostly tend to be unstable for any large masses when surrounded by an infinite bath of thermal radiation
In this analysis the turning point method is applied to the stability problem in both the microcanonical and the canonical ensembles, and we will show that stability changes appear in the latter case, which suggests that a Hawking– Page transition and a first order small black hole/large black hole phase transition occur in the system, similar to the one observed for charged and rotating black holes in AdS space [59,60,61,62,63]
In this paper we investigated the thermodynamic and stability properties of Kerr black holes described by the parametric, equilibrium- and zeroth law compatible Rényi entropy function
Summary
AdS ones, and in the standard black hole thermodynamic picture [6,7,8,9], they mostly tend to be unstable for any large masses when surrounded by an infinite bath of thermal radiation. By extending our previous investigations, we study the thermodynamic, stability and phase transition properties of Kerr black holes within the Rényi model and analyze whether similar results can be obtained to what we have found in the Schwarzschild case In this analysis the turning point method is applied to the stability problem in both the microcanonical and the canonical ensembles, and we will show that stability changes appear in the latter case, which suggests that a Hawking– Page transition and a first order small black hole/large black hole phase transition occur in the system, similar to the one observed for charged and rotating black holes in AdS space [59,60,61,62,63].
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