Black hole state counting in Loop Quantum Gravity: A number theoretical approach

TL;DR

This paper introduces a practical, exact method for computing black hole entropy in Loop Quantum Gravity, using number theory to analyze the spectrum of the area operator and solve the projection constraint.

Contribution

It provides a novel, computationally feasible approach to precisely count black hole microstates in Loop Quantum Gravity, including degeneracies and spectrum characterization.

Findings

Confirmed previous results on black hole degeneracy spectrum

Extended understanding of the spectrum's detailed structure

Provided an analytical solution to the projection constraint

Abstract

We give a practical method to exactly compute black hole entropy in the framework of Loop Quantum Gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and determine the number of solutions to the projection constraint analytically. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.