K-causality coincides with stable causality

TL;DR

This paper proves that K-causality is equivalent to stable causality and explores the relationship between various causal relations in spacetime, clarifying the hierarchy of causality conditions.

Contribution

It establishes the equivalence of K-causality and stable causality and links K^+ with Seifert's relation, clarifying the causal hierarchy.

Findings

K-causality coincides with stable causality

K^+ relation matches Seifert's relation in K-causal spacetimes

The causal condition hierarchy is clarified

Abstract

It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K^+ coincides with the Seifert's relation. As a consequence the causal relation "the spacetime is strongly causal and the closure of the causal relation is transitive" stays between stable causality and causal continuity.