Unique Carrollian manifolds emerging from Einstein spacetimes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866908821059796992 |
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| author | Blitz, S. McNutt, D. Nurowski, P. |
| author_facet | Blitz, S. McNutt, D. Nurowski, P. |
| contents | We explicitly determine all shear-free null hypersurfaces embedded in an Einstein spacetime, including vacuum asymptotically flat spacetimes. We characterize these hypersurfaces as oriented 3-dimensional manifolds where each is equipped with a coframe basis, a structure group and a connection. Such manifolds are known as null hypersurface structures (NHSs). The coframe and connection one-forms for an NHS appear as solutions to the projection of the Cartan structure equations onto the null hypersurface. We then show that each NHS corresponds to a Carrollian structure equipped with a unique pair of Ehresmann connection and affine connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unique Carrollian manifolds emerging from Einstein spacetimes Blitz, S. McNutt, D. Nurowski, P. General Relativity and Quantum Cosmology We explicitly determine all shear-free null hypersurfaces embedded in an Einstein spacetime, including vacuum asymptotically flat spacetimes. We characterize these hypersurfaces as oriented 3-dimensional manifolds where each is equipped with a coframe basis, a structure group and a connection. Such manifolds are known as null hypersurface structures (NHSs). The coframe and connection one-forms for an NHS appear as solutions to the projection of the Cartan structure equations onto the null hypersurface. We then show that each NHS corresponds to a Carrollian structure equipped with a unique pair of Ehresmann connection and affine connection. |
| title | Unique Carrollian manifolds emerging from Einstein spacetimes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2409.19682 |