Automorphic black holes as probes of extra dimensions

Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results with Langlandsʼ reciprocity conjecture to view black holes as probes of the geometry of spacetime. This point of view can be applied in any framework leading to automorphic forms, independently of the degree of supersymmetry of the models. In the present work we focus on the class of Chaudhuri–Hockney–Lykken compactifications defined as quotients associated to ZNZN groups. We show that the black hole entropy of these CHLNCHLN models can be derived from elliptic motives, thereby providing the simplest possible geometric building blocks of the Siegel type entropy count.