R\'enyi entropy and the thermodynamic stability of black holes

TL;DR

This paper explores how Rènyi entropy affects the thermodynamic stability of black holes, revealing conditions under which flat black holes can be stable and undergo phase transitions similar to those in anti-de Sitter space.

Contribution

It demonstrates that Rènyi entropy allows asymptotically flat black holes to achieve thermodynamic stability and exhibits a Hawking-Page-like phase transition depending on the Rènyi parameter.

Findings

Flat black holes can be thermodynamically stable with Rènyi entropy.

A Hawking-Page-like phase transition occurs at a critical temperature.

Stability is influenced by the Rènyi q-parameter.

Abstract

Thermodynamic stability of black holes, described by the R\'enyi 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 R\'enyi formula.