Non-imprisonment conditions on spacetime
arXiv:0712.3949 · doi:10.1063/1.2937907
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.
12 pages, 2 figures. v2: improved results on totally imprisoned curves, a figure changed, some misprints fixed