Geometric obstruction of black holes

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The completeness of the latter is then employed to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proof of these new results is preceded by a pedagogic review of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.