Affine connections for Galilean and Carrollian structures: a unified perspective
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913966917156864 |
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| author | Vigneron, Quentin Barzegar, Hamed Read, James |
| author_facet | Vigneron, Quentin Barzegar, Hamed Read, James |
| contents | We develop a classification of general Carrollian structures, permitting affine connections with both torsion and non-metricity. We compare with a recent classification of general Galilean structures in order to present a unified perspective on both. Moreover, we demonstrate how both sets of structures emerge from the most general possible Lorentzian structures in their respective limits, and we highlight the role of global hyperbolicity in constraining both structures. We then leverage this work in order to construct for the first time an ultra-relativistic geometric trinity of gravitational theories, and consider connections which are simultaneously compatible with Galilean and Carrollian structures. We close by outlining a number of open questions and future prospects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03936 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine connections for Galilean and Carrollian structures: a unified perspective Vigneron, Quentin Barzegar, Hamed Read, James General Relativity and Quantum Cosmology High Energy Physics - Theory We develop a classification of general Carrollian structures, permitting affine connections with both torsion and non-metricity. We compare with a recent classification of general Galilean structures in order to present a unified perspective on both. Moreover, we demonstrate how both sets of structures emerge from the most general possible Lorentzian structures in their respective limits, and we highlight the role of global hyperbolicity in constraining both structures. We then leverage this work in order to construct for the first time an ultra-relativistic geometric trinity of gravitational theories, and consider connections which are simultaneously compatible with Galilean and Carrollian structures. We close by outlining a number of open questions and future prospects. |
| title | Affine connections for Galilean and Carrollian structures: a unified perspective |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.03936 |