Intrinsic Timed Hausdorff Convergence and Its Implications

Abstract

Sakovich--Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov-Hausdorff distances and therefore extend naturally to a broader class of spaces. Here we show that, for timed-metric-spaces, intrinsic timed-Hausdorff convergence implies (timeless) Gromov-Hausdorff convergence as well as big bang convergence, among other related implications for future-developed convergence.