On the Causality and K-Causality between Measures

On the Causality and K-Causality between Measures

Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation K+ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “meas...

On the relationship between K-causality and infinite A-causality

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subset 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 obtai...

On the relationship between stable causality and K-causality

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 t...

K-causality coincides with stable causality

It is proven thatK-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.

Investigating The Co- Movement And Causality Between Iran And Germany