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 GromovHausdorff convergence based on the null distance in warped product Lorentzian length spaces and prove first results on its compatibility with synthetic curvature bounds.
 Publication:

Annales Henri Poincaré
 Pub Date:
 December 2022
 DOI:
 10.1007/s00023022011986
 arXiv:
 arXiv:2106.05393
 Bibcode:
 2022AnHP...23.4319K
 Keywords:

 Mathematics  Differential Geometry;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Metric Geometry;
 53C23;
 53C50;
 53B30;
 51K10;
 53C80
 EPrint:
 21 pages