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
Creators:	Creators Email ORCID Vigneron, Quentin quentin.vigneron@umk.pl Barzegar, Hamed hamed.barzegar@ens-lyon.fr Read, James james.read@philosophy.ox.ac.uk
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
Depositing User:	Dr. James Read
Date Deposited:	04 Jun 2025 13:04
Last Modified:	04 Jun 2025 13:04
Item ID:	25552
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Relativity Theory
Date:	3 June 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25552

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