Microcanonical distribution for black hole with allowance for nonadditivity

TL;DR

This paper explores how nonadditivity affects black hole statistical distributions, showing a transition from canonical to microcanonical form and linking black hole entropy to its area.

Contribution

It introduces a nonadditive microcanonical distribution for black holes and proposes a new entropy definition consistent with this distribution.

Findings

Black hole statistical weight is proportional to its area.

Distribution depends on nonadditive integrals of motion.

Entropy aligns with black hole area.

Abstract

It is shown that with allowance for nonadditivity the (canonical) distribution for a black hole transforms to a (microcanonical) distribution which depends on nonadditive integrals of the motion and represents a nonlinear function of energy - the square of black hole mass. From a comparison with the standard microcanonical distribution it is found that the statistical weight of black hole should be proportional to the black hole area. A definition of the black hole entropy consistent with the statistical weight is proposed.