On the nature of modified Rényi entropy and the incomplete statistics approach in black holes thermodynamics

¹ Departamento de Física, Universidade Federal Rural do Rio de Janeiro - 23890-971, Seropédica, RJ, Brazil
² Departamento de Física, Universidade Federal de Juiz de Fora - 36036-330, Juiz de Fora, MG, Brazil
³ Programa de Pós- Graduação Interdisciplinar em Física Aplicada, Instituto de Física, Universidade Federal do Rio de Janeiro - 21941-972, Rio de Janeiro, RJ, Brazil

^(a) evertonabreu@ufrrj.br (corresponding author)
^(b) jorge@fisica.ufjf.br

Received: 17 November 2020
Accepted: 9 April 2021

Abstract

In this work we have investigated the effects of the two highlighted non-Gaussian entropies which are the modified Rényi 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 λ-parameter and M, the BH mass, relative to a modified Rényi 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.