Journal
ANNALES HENRI POINCARE
Volume 23, Issue 12, Pages 4319-4342Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s00023-022-01198-6
Keywords
53C23; 53C50; 53B30; 51K10; 53C80
Funding
- University of Vienna
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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.
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.
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