On Quantum Statistical Mechanics of a Schwarzschild Black Hole

TL;DR

This paper uses non-perturbative quantum gravity and Chern-Simons theory to microscopically derive the thermodynamics of Schwarzschild black holes, showing that entropy is proportional to horizon area.

Contribution

It introduces a quantum geometric model for black hole thermodynamics using Chern-Simons states, linking microscopic quantum states to macroscopic entropy.

Findings

Black hole entropy is proportional to horizon area.

Quantum states are described by spin-labeled Chern-Simons theory.

The Chern-Simons level relates to the black hole's horizon area.

Abstract

Quantum theory of geometry, developed recently in the framework of non-perturbative quantum gravity, is used in an attempt to explain thermodynamics of Schwarzschild black holes on the basis of a microscopical (quantum) description of the system. We work with the formulation of thermodynamics in which the black hole is enclosed by a spherical surface B and a macroscopic state of the system is specified by two parameters: the area of the boundary surface and a quasilocal energy contained within. To derive thermodynamical properties of the system from its microscopics we use the standard statistical mechanical method of Gibbs. Under a certain number of assumptions on the quantum behavior of the system, we find that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B labelled with spins. The level of the Chern-Simons theory turns out to be proportional to the horizon area of black hole measured in Planck units. The statistical mechanical analysis turns out to be especially simple in the case when the entire interior of B is occupied by a black hole. We find in this case that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area.