The combinatorics of the SU(2) black hole entropy in loop quantum gravity

TL;DR

This paper employs combinatorial and number-theoretical techniques to analyze black hole entropy in loop quantum gravity, deriving asymptotic behavior, the Immirzi parameter, and logarithmic corrections.

Contribution

It introduces new generating functions for entropy calculation within a recent loop quantum gravity proposal, providing detailed asymptotic analysis.

Findings

Derived explicit generating functions for black hole entropy

Calculated the asymptotic behavior and Immirzi parameter

Identified the coefficient of the logarithmic correction

Abstract

We use the combinatorial and number-theoretical methods developed in previous work by the authors to study black hole entropy in the new proposal put forward by Engle, Noui and Perez. Specifically we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior including the value of the Immirzi parameter and the coefficient of the logarithmic correction.