Black Holes and Rings of minimal 5 - dim . Supergravity ∗

The aim of this talk is to address recent progress of 5-dimensional supergravity. We start with an issue related to the uniqueness theorem of black holes, which states that the most general 4-dim. black hole has to be of the Kerr-Newmann type, ie. is uniquely fixed by its conserved charges (mass, angular momentum, electric/magnetic charges) and the horizon topology is a 2-sphere [1, 2]. It implies especially that any wormhole has to be hidden behind a spherical horizon (topological censorship) and hence appears as a black hole for an outside observer. It fueled moreover the idea that stable microscopic black holes can regarded as elementary particles [3], which however is not (yet) realistic for different reasons, eg. there are no stable spinning black holes in four dimensions and moreover the mass to charge ratio is either not realistic or moduli dependent, but one should re-address this issue once all moduli are fixed. On the other hand, one can also ask, what happens in higher dimensions? Although the horizon geometry is still fixed by the conserved charges, the topology can be different. In five dimensions for examples, black rings with the geometry S1×S2 have been found [4, 5] and for D > 5, the allowed topology might be even more rich. This is in agreement with the general statement [6], that the horizon manifold has to have positive scalar curvature if the asymptotic vacuum is flat, which forbids in four dimensions, for example, a T 2 topology of a black hole horizon.