A Note on the Gannon-Lee Theorem

Abstract

We prove a Gannon-Lee theorem for non-globally hyperbolic Lo\-rentzian metrics of regularity $C^1$, the most general regularity class currently available in the context of the classical singularity theorems. Along the way we also prove that any maximizing causal curve in a $C^1$-spacetime is a geodesic and hence of $C^2$-regularity.

Final published version

References in corpus (3)

• Lorentz meets Lipschitz
• A note on causality conditions on covering spacetimes
• Causal simplicity and (maximal) null pseudoconvexity

Cited by in corpus (7)

• The singularity theorems of General Relativity and their low regularity extensions
• The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics
• A semiclassical singularity theorem
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• Hawking-type singularity theorems for worldvolume energy inequalities
• The codimension 2 null cut locus with applications to spacetime topology