Vigneron, Quentin and Barzegar, Hamed and Read, James (2025) Affine connections for Galilean and Carrollian structures: a unified perspective. [Preprint]
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Abstract
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.
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| Item Type: | Preprint | ||||||||||||
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| Additional Information: | Forthcoming in Classical and Quantum Gravity. | ||||||||||||
| Keywords: | Galilean spacetime, Carroll spacetime, affine connections, torsion, non-metricity, geometric trinity, global hyperbolicity | ||||||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Relativity Theory |
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| Depositing User: | Dr. James Read | ||||||||||||
| Date Deposited: | 31 Jul 2025 12:58 | ||||||||||||
| Last Modified: | 31 Jul 2025 12:58 | ||||||||||||
| Item ID: | 26071 | ||||||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Relativity Theory |
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| Date: | 3 June 2025 | ||||||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/26071 |
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Affine connections for Galilean and Carrollian structures: a unified perspective. (deposited 04 Jun 2025 13:04)
- Affine connections for Galilean and Carrollian structures: a unified perspective. (deposited 31 Jul 2025 12:58) [Currently Displayed]
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