GENERATING FUNCTIONS FOR BLACK HOLES IN LOOP QUANTUM GRAVITY

The computation of black hole entropy in loop quantum gravity requires the resolution of a combinatorial problem consisting in the counting of finite sequences of half integer numbers satisfying a condition involving the horizon area and the so called projection constraint. Recently this problem has been approached by using number theoretic methods based on the solution of certain diophantine equations. The nature of these equations is such that it is actually possible to write down generating functions to encode the solution to the counting problem. Here we report on this result and how it can be used to understand the detailed behavior of the black hole entropy according to loop quantum gravity.