Holographic bound in covariant loop quantum gravity

TL;DR

This paper explores the holographic bound in covariant loop quantum gravity by analyzing puncture statistics with Maxwell-Boltzmann and Bose-Einstein distributions, revealing entropy corrections and phase transition phenomena.

Contribution

It introduces formulae linking horizon area to holographic degrees of freedom and applies them to both Maxwell-Boltzmann and Bose-Einstein statistics in loop quantum gravity.

Findings

Holographic bound holds in the large area limit.

Entropy-area law correction is logarithmic in area.

Identification of phase transition related to Bose-Einstein condensate formation.

Abstract

We investigate puncture statistics based on the covariant area spectrum in loop quantum gravity. First, we consider Maxwell-Boltzmann statistics with a Gibbs factor for punctures. We establish formulae which relate physical quantities such as horizon area to the parameter characterizing holographic degrees of freedom. We also perform numerical calculations and obtain consistency with these formulae. These results tell us that the holographic bound is satisfied in the large area limit and correction term of the entropy-area law can be proportional to the logarithm of the horizon area. Second, we also consider Bose-Einstein statistics and show that the above formulae are also useful in this case. By applying the formulae, we can understand intrinsic features of Bose-Einstein condensate which corresponds to the case when the horizon area almost consists of punctures in the ground state. When this phenomena occurs, the area is approximately constant against the parameter characterizing the temperature. When this phenomena is broken, the area shows rapid increase which suggests the phase transition from quantum to classical area.