Using non-extensive statistical mechanics, the Bekenstein–Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero–Immirzi parameter ( γ ). The arbitrariness of γ is encoded in the strength of the “bias” created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of γ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.
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