On the nature of R\'enyi modified entropy and the Incomplete statistics approach in black holes thermodynamics

TL;DR

This paper explores how modified Rényi entropy and Incomplete statistics affect black hole thermodynamics, revealing conditions for stability and instability based on specific parameters.

Contribution

It introduces the application of two non-Gaussian entropies to black hole thermodynamics and analyzes their impact on stability criteria.

Findings

Heat capacities depend on entropy parameters and black hole mass.

Stability of black holes varies with entropy parameters.

Different entropies predict different stability regimes.

Abstract

In this work we have investigated the effects of the two highlighted nongaussian entropies which are the modified R\'enyi entropy and the so-called Incomplete statistics in the analysis of the thermodynamics of black holes (BHs). We have obtained the equipartition theorems and after that we obtained the heat capacities for both approaches. Depending on the values of both $\lambda-$parameter and $M$, the BH mass, relative to a modified R\'enyi entropy and, depending on the values of the $q-$parameter and $M$, the Incomplete entropy can determine if the BH has an unstable thermal equilibrium or not for each model.