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

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=ln⁡3/(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. Keywords: Loop Quantum Gravity, Immirzi parameter, Tsallis statistics