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., 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.

13 pages, no figures, to appear in Class. Quantum Grav

References in corpus (2)

• Black Holes in Higher Dimensions
• Chronological spacetimes without lightlike lines are stably causal

Cited by in corpus (7)

• The 1965 Penrose singularity theorem
• A Note on the Gannon-Lee Theorem
• On the geodesic incompleteness of spacetimes containing marginally outer trapped surfaces
• A note on causality conditions on covering spacetimes
• The codimension 2 null cut locus with applications to spacetime topology
• Rigidity aspects of Penrose's singularity theorem
• Some remarks on marginally trapped surfaces and geodesic incompleteness