Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06428 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914443751849984 |
|---|---|
| author | Müller, Olaf |
| author_facet | Müller, Olaf |
| contents | This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly causal Lorentzian manifolds to the corresponding category of Lorentzian spaces, and considers three problems in the context of maximal Cauchy developments of Lorentzian spaces: The first is to define pointed Gromov-Hausdorff metrics for spatially and temporally noncompact Lorentzian spaces, the second to present an explicit non-spacetime example of a maximal globally hyperbolic Lorentzian space, the third to define canonical representatives for Cauchy developments. A certain well-posedness property for geodesics plays a key role in each of the problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximality and Cauchy developments of Lorentzian length spaces Müller, Olaf Differential Geometry 53C99 This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly causal Lorentzian manifolds to the corresponding category of Lorentzian spaces, and considers three problems in the context of maximal Cauchy developments of Lorentzian spaces: The first is to define pointed Gromov-Hausdorff metrics for spatially and temporally noncompact Lorentzian spaces, the second to present an explicit non-spacetime example of a maximal globally hyperbolic Lorentzian space, the third to define canonical representatives for Cauchy developments. A certain well-posedness property for geodesics plays a key role in each of the problems. |
| title | Maximality and Cauchy developments of Lorentzian length spaces |
| topic | Differential Geometry 53C99 |
| url | https://arxiv.org/abs/2404.06428 |