Equilibrium Temperature for Black Holes with Nonextensive Entropy

TL;DR

This paper investigates the thermodynamic consistency of Hawking temperature with various nonextensive entropies, defining an effective equilibrium temperature and entropy, and highlighting the unique compatibility of Bekenstein-Hawking entropy.

Contribution

It introduces the concept of an effective equilibrium temperature for nonextensive entropies and clarifies the special role of Bekenstein-Hawking entropy in black hole thermodynamics.

Findings

Hawking temperature is inconsistent with most nonextensive entropies except Bekenstein entropy.

An effective equilibrium temperature can be defined for each nonextensive entropy.

Bekenstein-Hawking entropy uniquely satisfies the equilibrium condition for the Hawking temperature.

Abstract

Hawking temperature has been widely utilised in the literature as the temperature that corresponds to various nonextensive entropies. In this study, we analyze the compatibility of the Hawking temperature with the nonextensive entropies. We demonstrate that, for every nonextensive entropy, one may define an effective temperature (which we call equilibrium temperature) by utilizing the equilibrium condition, and that there is always an additive equilibrium entropy associated with this effective temperature. Except for Bekenstein entropy, we show that Hawking temperature is thermodynamically inconsistent with other nonextensive entropies. We focus on the equilibrium requirement for the Tsallis-Cirto black hole entropy and demonstrate that the Bekenstein-Hawking entropy is the related equilibrium entropy, and the Hawking temperature is the associated equilibrium temperature for the Tsallis-Cirto black hole entropy.