Black Hole State Counting in Loop Quantum Gravity: A Number-Theoretical Approach

We give an efficient method, combining number-theoretic and combinatorial ideas, 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 explicitly determine the number of solutions to the projection constraint. 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.

Figure 1

Plot of the black hole degeneracy as a function of the area (expressed in units of ${\ell }_P^2$ to facilitate the comparison with the results obtained in 4).