Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry

摘要

Using non-extensive statistical mechanics, the Bekenstein-Hawking area law isobtained from microstates of black holes in loop quantum gravity, for arbitraryreal positive values of the Barbero-Immirzi parameter$(\gamma)$. Thearbitrariness of $\gamma$ is encoded in the strength of the "bias" created inthe horizon microstates through the coupling with the quantum geometric fieldsexterior to the horizon. An experimental determination of $\gamma$ will fixthis coupling, leaving out the macroscopic area of the black hole to be theonly free quantity of the theory.