Horizon entropy with loop quantum gravity methods

TL;DR

This paper applies loop quantum gravity techniques to spherically symmetric isolated horizons, deriving a quantum description that recovers the Bekenstein-Hawking entropy law, and explores alternative quantization methods.

Contribution

It introduces a novel framework for describing isolated horizons using SU(2) connections and links it to 3d gravity quantization methods.

Findings

Horizon symplectic structure matches 3d gravity in first order form

Bekenstein-Hawking entropy law is recovered with imaginary Barbero-Immirzi parameter

Bulk excitations behave like particles in 3d gravity

Abstract

We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and a su(2) valued one form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similar to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.