The causal ladder and the strength of K-causality: II

Abstract

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 having 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.