On the computation of black hole entropy in loop quantum gravity

TL;DR

This paper introduces novel number-theoretical methods to compute black hole entropy in loop quantum gravity, providing exact integral expressions, comparing with prior results, and discussing asymptotic behavior.

Contribution

The authors develop new integral transform techniques for black hole entropy in loop quantum gravity, extending and correcting previous approaches by Meissner.

Findings

Confirmed some of Meissner's results

Extended the validity of previous formulas

Corrected certain mistakes in earlier work

Abstract

We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and also on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others, and correct some mistakes. At the end of the paper we will discuss the delicate issue of the asymptotics of black hole entropy.