Toward explaining black hole entropy quantization in loop quantum gravity

Understand

In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area.

• In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space.
• This formulation sheds some light on the origins of this step-like behavior of the entropy.
• In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy.