12:00
From the geometry of spacetime to the geometry of numbers
Abstract
One of the major open challenges in general relativity is the classification of black hole solutions in higher dimensional theories. I will explain a recent result in this direction in the context of Kaluza-Klein spacetimes admitting a sufficient number N of commuting U(1)-symmetries. It turns out that the black holes in such a theory are characterized by the usual asymptotic charges, together with certain combinatorical data and moduli. The combinatorial data characterize the nature of the U(1)^N-action, and its analysis is closely related to properties of integer lattices and questions in the area of geometric number theory. I will also explain recent results on extremal black holes which show that such objects display remarkable ``symmetry enhancement'' properties