ar X iv : g r - qc / 0 70 31 28 v 4 2 9 N ov 2 00 7 The causal ladder and the strength of K - causality . II

Hawking's stable causality implies Sorkin and Woolgar's K-causality. The work investigates the possible equivalence between the two causality requirements , an issue which was first considered by H. Seifert and then raised again by R. Low after the introduction of K-causality. First, a new proof is given that a spacetime is stably causal iff the Seifert causal relation is a partial order. It is then shown that given a K-causal spacetime and chosen an event, the light cones can be widened in a neighborhood of the event without spoiling K-causality. The idea is that this widening of the light cones can be continued leading to a global one. Unfortunately , due to some difficulties in the inductive process the author was not able to complete the program for a proof as originally conceived by H. Seifert. Nevertheless, it is proved that if K-causality coincides with stable causality then in any K-causal spacetime the K + future coincides with the Seifert future. Explicit examples are provided which show that the K + future may differ from the Seifert future in causal spacetimes.