A Note on the Gannon-Lee Theorem

Understand

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.