The c-completion of Lorentzian metric spaces

Abstract

Inspired by some Lorentzian versions of the notion of metric and length space
introduced by Kunzinger and S¨amman, and more recently, by Müller, and
Minguzzi and Sühr, we revisit the notion of Lorentzian metric space in order to
later construct the c-completion of these general objects. We not only prove that
this construction is feasible in great generality for these objects, including spacetimes
of low regularity, but also endow the c-completion with a structure of Lorentzian
metric space by itself. We also prove that the c-completion constitutes a well-suited
extension of the original space, which really completes it in a precise sense and
becomes sensible to certain causal properties of that space.

On the space of compact diamonds of Lorentzian length spaces

“…Non-timelike branching is an essential requirement in many important cases, like in the development of Lorentzian measure spaces [34]. Thus, our framework permits drawing relevant geometrical information even if branching is present, for instance, in the study of the causal completion [1,12].…”