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

TL;DR

This paper introduces a unifying framework for causal relations in spacetime, exploring the causal ladder from chronology to K-causality, and reveals new distinctions and properties within the hierarchy.

Contribution

It provides a novel characterization of the causal hierarchy, including the A-causality subladder, and demonstrates differences between K-causality and infinite A-causality with a spacetime example.

Findings

Closure of causal future is not transitive

Infinite A-causality subladder exists between strong causality and K-causality

K-causality differs from infinite A-causality in specific spacetime models

Abstract

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The causal hierarchy of spacetime is built from chronology up to K-causality and new characterizations of the distinction and strong causality properties are obtained. The closure of the causal future is not transitive, as a consequence its repeated composition leads to an infinite causal subladder between strong causality and K-causality - the A-causality subladder. A spacetime example is given which proves that K-causality differs from infinite A-causality.