Black holes quasinormal modes, Loop Quantum Gravity Immirzi parameter and nonextensive statistics

TL;DR

This paper explores how different statistical mechanics frameworks, including nonextensive Tsallis entropy, influence the determination of quantum properties of black holes in Loop Quantum Gravity, particularly the Immirzi parameter and minimal spin.

Contribution

It demonstrates that using Tsallis entropy alters the minimum spin value and the Immirzi parameter in black hole models within Loop Quantum Gravity.

Findings

Using Tsallis entropy changes the minimum spin value from 1.

The Immirzi parameter depends on the nonextensive q-parameter.

Different statistical frameworks affect black hole quantum properties.

Abstract

It is argued that, using the black hole area entropy law together with the Boltzmann-Gibbs statistical mechanics and the quasinormal modes of the black holes, it is possible to determine univocally the lowest possible value for the spin $j$ in the context of the Loop Quantum Gravity theory which is $j_{min}=1$. Consequently, the value of Immirzi parameter is given by $\gamma = \ln 3/(2\pi\sqrt{2})$. In this paper, we have shown that if we use Tsallis microcanonical entropy rather than Boltzmann-Gibbs framework then the minimum value of the label $j$ depends on the nonextensive $q$-parameter and may have values other than $j_{min}=1$.