The annoying null boundaries

TL;DR

This paper investigates the boundary properties of certain expanding singularity space-times, proving the non-existence of continuous extensions across compact boundaries and characterizing the boundary as null where differentiable.

Contribution

It establishes new results on the boundary structure of expanding singularity space-times, particularly regarding extension impossibility and boundary nullity in non-compact cases.

Findings

No $C^0$-extensions across compact boundaries exist.

Boundaries are null where differentiable in non-compact space-times.

Results apply under specific assumptions on expanding singularities.

Abstract

We consider a class of globally hyperbolic space-times with "expanding singularities". Under suitable assumptions we show that no $C^0$-extensions across a compact boundary exist, while the boundary must be null wherever differentiable (which is almost everywhere) in the non-compact case.