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.

arXiv comment21 pages

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Cited by in corpus (15)

• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• A Lorentzian analog for Hausdorff dimension and measure
• Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
• The Null distance encodes causality
• Global Hyperbolicity through the Eyes of the Null Distance
• Time functions on Lorentzian length spaces
• Gluing constructions for Lorentzian length spaces
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• Causal completions as Lorentzian pre-length spaces
• Gluing of Lorentzian length spaces and the causal ladder
• Optimal transport on null hypersurfaces and the null energy condition
• A lower semicontinuous time separation function for $C^0$ spacetimes
• A Toponogov globalisation result for Lorentzian length spaces
• Spacetime closedness theorem for homogeneous Lorentzian foliations