Microcanonical statistics of black holes and bootstrap condition

TL;DR

This paper analyzes the microcanonical statistics of Schwarzschild and Reissner-Nordström black holes, demonstrating that at high energy, a single black hole dominates, satisfying the bootstrap condition without charge breaking this property.

Contribution

It establishes inequalities in the microcanonical density of states for black holes and shows they obey the bootstrap condition even with charge.

Findings

Most probable configuration is a single black hole with all mass and charge.

Black holes obey the bootstrap condition at high energy.

U(1) charge does not break the bootstrap property.

Abstract

The microcanonical statistics of the Schwarzschild black holes as well as the Reissner-Nordstr$\sf \ddot{o}$m black holes are analyzed. In both cases we set up the inequalities in the microcanonical density of states. These are then used to show that the most probable configuration in the gases of black holes is that one black hole acquires all of the mass and all of the charge at high energy limit. Thus the black holes obey the statistical bootstrap condition and, in contrast to the other investigation, we see that U(1) charge does not break the bootstrap property.