Initial data sets with dominant energy condition admitting no smooth dec spacetime extension
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913725882040320 |
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| author | Glöckle, Jonathan |
| author_facet | Glöckle, Jonathan |
| contents | There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any embedded spacelike hypersurface. In this article, we discuss the question of a potential converse of this: Is every dec initial data set the induced one on a spacelike hypersurface within a suitably chosen dec Lorentzian manifold? We provide an example showing that in general the answer is no if we require all structures to be smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Initial data sets with dominant energy condition admitting no smooth dec spacetime extension Glöckle, Jonathan General Relativity and Quantum Cosmology Differential Geometry There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any embedded spacelike hypersurface. In this article, we discuss the question of a potential converse of this: Is every dec initial data set the induced one on a spacelike hypersurface within a suitably chosen dec Lorentzian manifold? We provide an example showing that in general the answer is no if we require all structures to be smooth. |
| title | Initial data sets with dominant energy condition admitting no smooth dec spacetime extension |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2308.00643 |