Null distance and convergence of Lorentzian length spaces

Abstract

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.

21 pages

References in corpus (1)

• Spacetime distances: an exploration

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• Causal completions as Lorentzian pre-length spaces
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• Spacetime closedness theorem for homogeneous Lorentzian foliations