Existence of a Semiclassical Approximation in Loop Quantum Gravity

TL;DR

This paper demonstrates a semiclassical approximation in loop quantum gravity by applying Bohr-Sommerfeld quantization to a black hole model, deriving entropy consistent with Bekenstein-Hawking, and independently determining the Barbero-Immirzi parameter.

Contribution

It provides evidence for a semiclassical limit in loop quantum gravity and offers a novel derivation of the Barbero-Immirzi parameter using black hole entropy.

Findings

Entropy matches Bekenstein-Hawking formula

Semiclassical limit exists in loop quantum gravity

Barbero-Immirzi parameter derived independently

Abstract

We consider a spherical symmetric black hole in the Schwarzschild metric and apply Bohr-Sommerfeld quantization to determine the energy levels. The canonical partition function is then computed and we show that the entropy coincides with the Bekenstein-Hawking formula when the maximal number of states for the black hole is the same as computed in loop quantum gravity, proving in this case the existence of a semiclassical limit and obtaining an independent derivation of the Barbero-Immirzi parameter.