Alternative entropies and consistent black hole thermodynamics

TL;DR

This paper investigates the conditions under which alternative entropy measures like Rényi and Tsallis can be integrated into consistent black hole thermodynamics, especially in modified gravity scenarios, aligning with classical results.

Contribution

It demonstrates how alternative entropies can be incorporated into black hole thermodynamics for specific modified gravity models, expanding the understanding beyond Bekenstein-Hawking entropy.

Findings

Alternative entropies can be consistent with black hole thermodynamics in certain modified gravity cases.

Black hole masses and temperatures can match those derived from Bekenstein-Hawking entropy.

Examples show equivalence of alternative and traditional entropy-based thermodynamics under specific conditions.

Abstract

While the Bekenstein-Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (R\'enyi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein-Hawking entropy.