Lorentzian metric spaces and their Gromov-Hausdorff convergence (Q6561407)

This paper is devoted to the development of a Lorentzian signature version of the by now classical theory of metric geometry, obtaining results on sectional curvature bounds via comparison geometry, as obtained by the A. D. Alexandrov school in the Riemannian setting.\N\NThe authors introduce a notion of bounded Lorentzian metric space \((X,d)\) that generalizes causally convex subsets of globally hyperbolic spacetimes. They derive the topology, the chronological relation and the causal relation from just \((X, d)\), without the need of a background distance or order relation. Moreover, they define Gromov-Hausdorff convergence and show that two bounded Lorentzian metric spaces at zero Gromov-Hausdorff distance are indeed isometric and homeomorphic.