On the topology of stationary black holes

We prove that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected. Under suitable additional hypotheses, this implies, in particular, that each connected component of a cross-section of the event horizon of a stationary black hole must have spherical topology. 1 Introduction The theory of the uniqueness of stationary black holes in classical general relativity intertwines the global techniques of differential geometry with those of the theory of geometric partial differential equations. In spite of considerable progress in the understanding of the issues involved, several open questions in that theory still remain (cf. e.g. 4 for a recent 1 review). As has been recently stressed by Galloway 8, one of those is the expected spherical topology of connected components of spacelike sections of event horizons. Recall that such a claim has been made in 12, 11, but, as discussed in detail in 8...