Causal conditions fail along a null geodesic (Q1999807)

It is well known that the failure of strong causality to hold at one point entails the failure along an entire null geodesic segment. A similar statement is true for the property of being distinguishing. In this paper, the authors systematically study this implication also for other causality properties. They are able to show that it also applies for causal continuity and stable causality. They comment on other causality properties as well, and point out possible applications to the analysis of spacetime-singularities.