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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Detalles Bibliográficos
Autores principales: Kunzinger, Michael, Steinbauer, Roland
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9674770/
https://www.ncbi.nlm.nih.gov/pubmed/36415328
http://dx.doi.org/10.1007/s00023-022-01198-6
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author Kunzinger, Michael
Steinbauer, Roland
author_facet Kunzinger, Michael
Steinbauer, Roland
author_sort Kunzinger, Michael
collection PubMed
description 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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spelling pubmed-96747702022-11-20 Null Distance and Convergence of Lorentzian Length Spaces Kunzinger, Michael Steinbauer, Roland Ann Henri Poincare Original Paper 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. Springer International Publishing 2022-05-31 2022 /pmc/articles/PMC9674770/ /pubmed/36415328 http://dx.doi.org/10.1007/s00023-022-01198-6 Text en © The Author(s) 2022, corrected publication 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Kunzinger, Michael
Steinbauer, Roland
Null Distance and Convergence of Lorentzian Length Spaces
title Null Distance and Convergence of Lorentzian Length Spaces
title_full Null Distance and Convergence of Lorentzian Length Spaces
title_fullStr Null Distance and Convergence of Lorentzian Length Spaces
title_full_unstemmed Null Distance and Convergence of Lorentzian Length Spaces
title_short Null Distance and Convergence of Lorentzian Length Spaces
title_sort null distance and convergence of lorentzian length spaces
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9674770/
https://www.ncbi.nlm.nih.gov/pubmed/36415328
http://dx.doi.org/10.1007/s00023-022-01198-6
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