Barrow's black hole entropy and the equipartition theorem

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
⁴ Departamento de Física, Universidade do Estado do Rio Grande do Norte - 59610-210, Mossoró, RN, Brazil

^(a) evertonabreu@ufrrj.br
^(b) jorge@fisica.ufjf.br
^(c) edesiobarboza@uern.br

Received: 23 May 2020
Accepted: 5 June 2020

Abstract

Barrow's entropy appears due to the fact that the black hole surface can be modified due to the quantum gravitational outcome. The measure of this perturbation is given by a new exponent Δ. In this letter we have shown that, from the standard mathematical form of the equipartition theorem, we can relate it to Barrow's entropy. After that, we tested the thermodynamical coherence of the system by calculating exactly the heat capacity which established an interval of the possible thermodynamical coherent values of the Barrow entropic exponent.