Quantum Geometry and Black Hole Entropy

TL;DR

This paper introduces a quantum gravity framework where black hole entropy is derived from a Chern-Simons theory on the horizon, aligning with the Bekenstein-Hawking formula through the Immirzi parameter.

Contribution

It establishes a non-perturbative quantum gravity model linking black hole entropy to horizon area via Chern-Simons theory and the Immirzi parameter.

Findings

Black hole degrees of freedom described by Chern-Simons theory

Black hole entropy proportional to horizon area

Matching Bekenstein-Hawking formula with specific Immirzi parameter

Abstract

A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large non-rotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the Bekenstein-Hawking formula S = A/4*l_p^2. With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charge, which are not necessarily near extremal.