Causally simple inextendible spacetimes are hole-free

TL;DR

This paper proves that causally simple inextendible spacetimes are free of holes, confirming that causal simplicity ensures spacetime completeness, with implications for understanding causal discontinuities.

Contribution

It establishes that causally simple inextendible spacetimes are hole-free, showing causal simplicity's role in preventing spacetime holes and highlighting its optimality.

Findings

Causally simple inextendible spacetimes are hole-free.

Causal simplicity cannot be weakened to causal continuity.

Discontinuities in causal relations relate to incomplete development of hypersurfaces.

Abstract

It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to causal continuity. Physically, it means that if there is some partial Cauchy hypersurface which, for some reason, does not fully develop its influence, then there is some discontinuity in the causal relation.