On the Gannon–Lee singularity theorem in higher dimensions

Abstract

The Gannon–Lee singularity theorems give well-known restrictions on the spatial topology of singularity-free (i.e. non-spacelike 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.