On the Gannon-Lee Singularity Theorem in Higher Dimensions

TL;DR

This paper revisits the Gannon-Lee singularity theorems, extending their scope to higher-dimensional spacetimes by relaxing global hyperbolicity and accommodating more complex spatial topologies.

Contribution

It broadens the classical results by weakening assumptions and adapting to the richer topological structures possible in higher dimensions.

Findings

Classical singularity theorems are extended to higher dimensions.

Global hyperbolicity requirement is relaxed in the new results.

Richer spatial topologies are compatible with singularity theorems in higher dimensions.

Abstract

The Gannon-Lee singularity theorems give well-known restrictions on the spatial topology of singularity-free (i.e., nonspacelike geodesically complete), globally hyperbolic spacetimes. In this paper, we revisit these classic results in the light of recent developments, especially the failure in higher dimensions of a celebrated theorem by Hawking on the topology of black hole horizons. The global hyperbolicity requirement is weakened, and we expand the scope of the main results to allow for the richer variety of spatial topologies which are likely to occur in higher-dimensional spacetimes.