---
author:
- 'Viktor G. Czinner'
- and Hideo Iguchi
title: 'Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics'
---

Introduction
============

Gravitational phase transitions, in particular the ones connected to black hole thermodynamics, are essential constituents of many open problems in modern theoretical physics. The Hawking–Page phase transition [@Hawking:1982dh] of black holes in anti-de Sitter space is one of the most important ones due to its role in the AdS/CFT correspondence [@Maldacena:1997re; @Witten:1998qj] and also in related phenomena of confinement/deconfinement transitions at finite temperature in various gauge theories [@MMT1; @MMT2]. Because of the different background geometry, asymptotically flat black holes have different stability properties than AdS ones, and in the standard black hole thermodynamic picture [@Bekenstein:1973ur; @Bardeen:1973gs; @Hawking:1974sw; @Hawking:1976de], they mostly tend to be unstable for any large masses when surrounded by an infinite bath of thermal radiation. A Hawking–Page transition does not occur under these conditions, and a cosmic black hole nucleation is not present in asymptotically flat spacetimes. Apart from the gravity interest, the above phenomenon is interesting from a thermodynamic viewpoint as well, and for a clear understanding of the physics behind, the underlying theory of black hole thermodynamics is also necessary 