Black Hole Thermodynamics via Tsallis Statistical Mechanics

TL;DR

This paper explores black hole thermodynamics using Tsallis non-extensive statistical mechanics, deriving modified entropy expressions that suggest black hole stabilization and bounds on non-extensive parameters.

Contribution

It introduces a novel approach to black hole entropy by applying Tsallis statistical mechanics, highlighting the effects of non-extensivity on black hole stability.

Findings

Black hole entropy is modified by non-extensive effects.

Non-extensivity can stabilize black holes.

Bounds on the Tsallis parameter are established.

Abstract

An investigation of black hole thermodynamics based on Tsallis statistical mechanics is explored through the study of the thermodynamics of a gas system located near the horizon of a black hole. In spite of the difficulty in exploring black hole thermodynamics through statistical mechanics, the entropy of the nearby gas system is found to be proportional to the black hole's horizon area using Gibbs-Boltzmann statistical mechanics. This allows us to study black hole thermodynamics by using statistical mechanics through the thermodynamic behaviors of the gas system. Since the entropy of the black hole is proportional to the horizon area, it is more suitable to use non-extensive statistical mechanics instead of the usual Gibbs-Boltzmann ones. In this work, the black hole entropy is derived based on Tsallis statistical mechanics, one of well-known non-extensive statistical mechanics. It is found that the black hole entropy gets a modification due to non-extensivity. By using such an entropy, the black hole can be stabilized due to the non-extensivity, and the bound on the non-extensive parameter is also determined.