In smooth/C^{1,1} Lorentzian spacetimes, future/past chrono- and causalcompleteness and bounded directed order completeness are all equivalent to global hyperbolicity.
Non-imprisonment conditions on spacetime
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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.
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Global hyperbolicity meets order completeness
In smooth/C^{1,1} Lorentzian spacetimes, future/past chrono- and causalcompleteness and bounded directed order completeness are all equivalent to global hyperbolicity.