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 st...

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Bibliographic Details
Published in:Annales Henri Poincaré 2022, Vol.23 (12), p.4319-4342
Main Authors: Kunzinger, Michael, Steinbauer, Roland
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Convergence
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Original Paper
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
Topology
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Summary: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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-022-01198-6