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

Abstract

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M × 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.