Barrow black hole corrected-entropy model and Tsallis nonextensivity

TL;DR

This paper explores the effects of quantum fluctuations on Barrow black hole entropy using Tsallis nonextensive thermodynamics, analyzing stability and thermodynamic properties with a new generalized equipartition law.

Contribution

It introduces a master equation for the equipartition law incorporating Tsallis' nonextensivity into quantum-corrected Barrow entropy, analyzing stability across various parameters.

Findings

Derived a generalized equipartition law for Barrow black holes with Tsallis q-parameter.

Analyzed thermal stability as a function of quantum fluctuation and nonextensivity parameters.

Identified conditions for stability and phase transitions in the black hole thermodynamics.

Abstract

The quantum scenario concerning Hawking radiation, gives us a precious clue that a black hole has its temperature directly connected to its area gravity and that its entropy is proportional to the horizon area. These results have shown that there exist a deep association between thermodynamics and gravity. The recently introduced Barrow formulation of back holes entropy, influenced by the spacetime geometry, shows the quantum fluctuations effects through Barrow exponent, $\Delta$, where $\Delta=0$ represents the usual spacetime and its maximum value, $\Delta=1$, characterizes a fractal spacetime. The quantum fluctuations are responsible for such fractality. Loop quantum gravity approach provided the logarithmic corrections to the entropy. This correction arises from quantum and thermal equilibrium fluctuations. In this paper we have analyzed the nonextensive thermodynamical effects of the quantum fluctuations upon the geometry of a Barrow black hole. We discussed the Tsallis' formulation of this logarithmically corrected Barrow entropy to construct the equipartition law. Besides, we obtained a master equation that provides the equipartition law for any value of the Tsallis $q$-parameter and we analyzed several different scenarios. After that, the heat capacity were calculated and the thermal stability analysis was carried out as a function of the main parameters, namely, one of the so-called pre-factors, $q$ and $\Delta$.