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 Sämman [24], and more recently, by Müller [31], and Minguzzi and Sühr [30], 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.