Quantum black holes, partition of integers and self-similarity

Abstract

We take the view that the area of a black hole's event horizon is quantized, $A=l_P^2(4\ln 2)N$, and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, $S_{BH}$, 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 $N$. Hence we construct from there a composition law between the sub-parts 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 $N$. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, that necessarily require different (quantum) statistical weights for the various configurations.

8 pages, no figures

References in corpus (1)

• The physical interpretation of the spectrum of black hole quasinormal modes

Cited by in corpus (2)

• Hunting Quantum Gravity with Analogs: the case of graphene
• Quantum black holes as classical space factories