Area-law versus R\'enyi and Tsallis black hole entropies

TL;DR

This paper examines Rényi and Tsallis entropies as alternatives to the traditional black hole entropy, analyzing their consistency with thermodynamics and potential links to quantum gravity corrections.

Contribution

It explores the compatibility of Rényi and Tsallis entropies with black hole thermodynamics and their relation to quantum gravity modifications.

Findings

Replacing entropy notions can lead to thermodynamic inconsistencies.

Rényi and Tsallis entropies may be related to quantum gravity corrected entropies.

Thermodynamic stability depends on the entropy definition used.

Abstract

The R\'enyi and Tsallis entropies are discussed as possible alternatives to the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the entropy notion, but not the Hawking temperature and the thermodynamical energy may render the whole black hole thermodynamics inconsistent. The possibility to relate the R\'enyi and Tsallis entropies with the quantum gravity corrected Bekenstein-Hawking entropy is discussed.