Results on Lorentzian metric spaces
Published: Oct 28, 2025
Last Updated: Oct 28, 2025
Authors:E. Minguzzi
Abstract
We provide a short introduction to ``Lorentzian metric spaces" i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed, such as the continuity of the Lorentzian distance and the relative compactness of chronological diamonds. The latter condition is natural for interpreting these spaces as low-regularity versions of globally hyperbolic spacetimes. Confirming this interpretation, we prove that every Lorentzian metric space admits a Cauchy time function. The proof is constructive for this general setting and it provides a novel argument that is interesting already for smooth spacetimes.