Barrow fractal entropy and the black hole quasinormal modes

Abstract

Using the Boltzmann-Gibbs statistical mechanics together with the quasinormal modes of the black holes and the Bekenstein-Hawking area entropy law, we can determine univocally the lowest possible value for the spin j, which is jmin=1, in the framework of the Loop Quantum Gravity theory. Subsequently, the value of Immirzi parameter is given by γ=ln⁡3/(2π2). In this paper, we have demonstrated that if we use the Barrow formulation for the black hole entropy then the minimum value of the label j depends on the value, which characterizes the fractal structure of the black hole surface called Δ parameter, and may have values other than jmin=1.