Quantum black holes, partition of integers and self-similarity

Abstract

In this paper, we take the view that the area of a black hole’s event horizon is quantized, [Formula: see text], and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, [Formula: see text], our main focus being black hole self-similarity. We first find a two-to-one map between the black hole’s configurations and the ordered partitions of the integer [Formula: see text]. Hence, we construct from there a composition law between the subparts making the whole configuration space. This gives meaning to black hole self-similarity, entirely within a single description, as a phenomenon stemming from the well-known self-similarity of the ordered partitions of [Formula: see text]. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, which necessarily require different (quantum) statistical weights for the various configurations.