Geometric obstruction of black holes

TL;DR

This paper investigates how sectional curvature bounds influence the global structure of Lorentzian manifolds, proving completeness and black hole absence in certain cosmological and static spacetimes, with implications for higher-dimensional theories.

Contribution

It provides new completeness theorems for specific Lorentzian geometries and rigorously shows the non-existence of static spherically symmetric black holes beyond three dimensions.

Findings

Proves completeness of homogeneous and isotropic cosmologies.

Establishes absence of static spherically symmetric black holes in higher dimensions.

Extends local sectional curvature bounds to global geometric properties.

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.