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 jmin=1. Consequently, the value of Immirzi parameter is given by γ=ln3/(2π2). 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 jmin=1.
Highlights
Loop Quantum Gravity (LQG)[1] is a theory of quantum gravity that proposes to unify quantum field theory and general relativity
We have shown that if we use Tsallis microcanonical entropy rather than Boltzmann-Gibbs framework the minimum value of the label j depends on the nonextensive q-parameter and may have values other than jmin = 1
The Hilbert space of LQG is formed by spin networks which are graphs with edges that carry labels such as j = 0, 1/2, 1, 3/2, . . . . In LQG, the area of a given region of space has a discrete spectrum in such a way that, if a surface is intersected or punctured by the spin network edge that carries the label j, the surface carries an area element written as [2,3,4]
Summary
Loop Quantum Gravity (LQG)[1] is a theory of quantum gravity that proposes to unify quantum field theory and general relativity. Loop Quantum Gravity Immirzi parameter and nonextensive statistics C. Abreu,1, 2, 3, ∗ Jorge Ananias Neto,2, † Edesio M.
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