Statistical Mechanics of Black Holes

TL;DR

This paper explores the statistical mechanics of black hole gases, revealing that equilibrium is dominated by a single black hole, with implications for black hole thermodynamics and quantum coherence.

Contribution

It demonstrates that the microcanonical ensemble is the appropriate framework and shows Schwarzschild black holes satisfy the bootstrap condition, advancing understanding of black hole thermodynamics.

Findings

Equilibrium configuration involves most energy in a single black hole

Microcanonical temperature matches Hawking temperature of the largest black hole

U(1) charges disrupt the bootstrap property

Abstract

We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried by a single black hole. Schwarzschild black holes are found to obey the statistical bootstrap condition. In all cases, the microcanonical temperature is identical to the Hawking temperature of the most massive black hole in the gas. U(1) charges in general break the bootstrap property. The problems of black hole decay and of quantum coherence are also addressed.