Geometric obstruction of black holes

Abstract

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 latter result is used to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proofs of these new results are preceded by a detailed exposition of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.

50 pages, 2 figures

References in corpus (2)

• Sectional Curvature Bounds in Gravity: Regularisation of the Schwarzschild Singularity
• Classical limit of quantum gravity in an accelerating universe

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