Statistical analysis of entropy correction from topological defects in Loop Black Holes

TL;DR

This paper analyzes the entropy of quantum black holes in Loop Quantum Gravity, considering punctures as quantum hair, and derives corrections to the Bekenstein-Hawking law in the grand canonical ensemble.

Contribution

It introduces a grand canonical ensemble approach to black hole entropy in LQG, revealing new entropy corrections and relations involving the Barbero-Immirzi parameter.

Findings

Entropy depends on average area and punctures

Leading order matches Bekenstein-Hawking law with fixed gamma

Sub-leading correction differs in sign from microcanonical results

Abstract

In this paper we discuss the entropy of quantum black holes in the LQG formalism when the number of punctures on the horizon is treated as a quantum hair, that is we compute the black hole entropy in the grand canonical (area) ensemble. The entropy is a function of both the average area and the average number of punctures and bears little resemblance to the Bekenstein-Hawking entropy. In the thermodynamic limit, both the "temperature" and the chemical potential can be shown to be functions only of the average area per puncture. At a fixed temperature, the average number of punctures becomes proportional to the average area and we recover the Bekenstein-Hawking area-entropy law to leading order provided that the Barbero-Immirzi parameter, $\gamma$, is appropriately fixed. This also relates the chemical potential to $\gamma$. We obtain a sub-leading correction, which differs in signature from that obtained in the microcanonical and canonical ensembles in its sign but agrees with earlier results in the grand canonical ensemble.