Null Distance and Convergence of Lorentzian Length Spaces

The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize Lorentzian causality theory beyond the manifold level. We then study Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and prove first results on its compatibility with synthetic curvature bounds.

Automated summary

The null distance proposed by Sormani and Vega encodes both the manifold topology and the causality structure of a smooth spacetime. This concept is extended to Lorentzian length spaces, which generalize the Lorentzian causality theory beyond the manifold level. The article also investigates Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and provides initial results regarding its compatibility with synthetic curvature bounds.