Non-imprisonment conditions on spacetime

TL;DR

This paper investigates non-imprisonment conditions in spacetimes, establishing their relationship with causal properties and analyzing the structure of imprisoned causal curves to enhance understanding of the causal hierarchy.

Contribution

It proves that non-partial imprisonment implies distinction and that feeble distinction implies non-total imprisonment, integrating non-imprisonment conditions into the causal ladder.

Findings

Non-partial imprisonment implies the distinction property.

Feeble distinction implies non-total imprisonment.

Results on minimal invariant sets of imprisoned causal curves.

Abstract

The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proved that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a result the non-imprisonment conditions can be included in the causal ladder of spacetimes. Finally, totally imprisoned causal curves are studied in detail, and results concerning the existence and properties of minimal invariant sets are obtained.