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

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.