Entropy calculation for a toy black hole

The present paper is concerned with the description of black holes and calculation of their entropy in the framework of loop quantum gravity (see [1, 2] for some general introduction to loop quantum gravity). The literature on this subject is large and includes (but is by no means limited to) the pioneering work [3], the introduction of a precise formalism [4, 5], the reformulation and approximate solution of the combinatorial problems involved [6, 7]. Although the basics are by now quite well understood, there still are surprises in store. One example are the structures that were found in a computer analysis of the spectrum of states [18, 19].