On homogeneous 3-dimensional spacetimes: focus on plane waves
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909469669064704 |
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| author | Allout, Souheib Belkacem, Abderrahmane Zeghib, Abdelghani |
| author_facet | Allout, Souheib Belkacem, Abderrahmane Zeghib, Abdelghani |
| contents | We revisit the classification of Lorentz homogeneous spaces of dimension $3$, and relax usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmetric nor locally isometric to a left-invariant Lorentz metric on a $3$-dimensional Lie group. We characterize homogeneous plane waves in dimension $3$, and prove they are non-extendable, and geodesically complete only if they are symmetric. Finally, only one non-flat plane wave has a compact model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11439 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On homogeneous 3-dimensional spacetimes: focus on plane waves Allout, Souheib Belkacem, Abderrahmane Zeghib, Abdelghani Differential Geometry We revisit the classification of Lorentz homogeneous spaces of dimension $3$, and relax usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmetric nor locally isometric to a left-invariant Lorentz metric on a $3$-dimensional Lie group. We characterize homogeneous plane waves in dimension $3$, and prove they are non-extendable, and geodesically complete only if they are symmetric. Finally, only one non-flat plane wave has a compact model. |
| title | On homogeneous 3-dimensional spacetimes: focus on plane waves |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2210.11439 |