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Lorentzian length spaces

We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way, we recover many fundamental results in greater...

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Detalles Bibliográficos
Autores principales: Kunzinger, Michael, Sämann, Clemens
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6397614/
https://www.ncbi.nlm.nih.gov/pubmed/30894782
http://dx.doi.org/10.1007/s10455-018-9633-1
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author Kunzinger, Michael
Sämann, Clemens
author_facet Kunzinger, Michael
Sämann, Clemens
author_sort Kunzinger, Michael
collection PubMed
description We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way, we recover many fundamental results in greater generality, while at the same time clarifying the minimal requirements for and the interdependence of the basic building blocks of the theory. A main focus of this work is the introduction of synthetic curvature bounds, akin to the theory of Alexandrov and CAT(k)-spaces, based on triangle comparison. Applications include Lorentzian manifolds with metrics of low regularity, closed cone structures, and certain approaches to quantum gravity.
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spelling pubmed-63976142019-03-18 Lorentzian length spaces Kunzinger, Michael Sämann, Clemens Ann Glob Anal Geom (Dordr) Article We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way, we recover many fundamental results in greater generality, while at the same time clarifying the minimal requirements for and the interdependence of the basic building blocks of the theory. A main focus of this work is the introduction of synthetic curvature bounds, akin to the theory of Alexandrov and CAT(k)-spaces, based on triangle comparison. Applications include Lorentzian manifolds with metrics of low regularity, closed cone structures, and certain approaches to quantum gravity. Springer Netherlands 2018-10-05 2018 /pmc/articles/PMC6397614/ /pubmed/30894782 http://dx.doi.org/10.1007/s10455-018-9633-1 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Kunzinger, Michael
Sämann, Clemens
Lorentzian length spaces
title Lorentzian length spaces
title_full Lorentzian length spaces
title_fullStr Lorentzian length spaces
title_full_unstemmed Lorentzian length spaces
title_short Lorentzian length spaces
title_sort lorentzian length spaces
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6397614/
https://www.ncbi.nlm.nih.gov/pubmed/30894782
http://dx.doi.org/10.1007/s10455-018-9633-1
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