Time functions and $K$-causality between measures

Abstract

Employing the notion of a coupling between measures, drawn from the optimal transport theory, we study the extension of the Sorkin-Woolgar causal relation $K^{+}$ onto the space $\mathcal{P}(\mathcal{M})$ of Borel probability measures on a given spacetime $\mathcal{M}$. We show that Minguzzi's characterization of $K^{+}$ in terms of time functions possesses a "measure-theoretic" generalization. Moreover, we prove that the relation $K^{+}$ extended onto $\mathcal{P}(\mathcal{M})$ retains its property of antisymmetry for $\mathcal{M}$ stably causal.

10 pages, contribution to the proceedings of the meeting "Non-regular Spacetime Geometry", 20-22 June 2017, Florence, Italy

References in corpus (3)

• Causality for nonlocal phenomena
• Causal evolution of wave packets
• Polish spaces of causal curves

Cited by in corpus (1)

• Generally covariant $N$-particle dynamics