A note on the Gannon–Lee theorem

Abstract

AbstractWe prove a Gannon–Lee theorem for non-globally hyperbolic Lorentzian metrics of regularity $$C^1$$ 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 $$C^1$$ C 1 -spacetime is a geodesic and hence of $$C^2$$ C 2 -regularity.