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

TL;DR

This paper explores the relationship between K-causality and stable causality in spacetime, providing new proofs and examples to clarify their equivalence and differences, advancing understanding in causal structure theory.

Contribution

It offers a new proof linking stable causality to the Seifert relation and investigates conditions under which K-causality and stable causality are equivalent, including explicit counterexamples.

Findings

Stable causality iff Seifert relation is a partial order

Light cone widening preserves K-causality locally

K-future may differ from Seifert future in some spacetimes

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 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 relation in causal spacetimes.