The authors classify general Carrollian affine connections with torsion and non-metricity, show their emergence from Lorentzian limits, and build an ultra-relativistic geometric trinity of gravity theories.
Teleparallel Newton--Cartan gravity
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abstract
We discuss a teleparallel version of Newton--Cartan gravity. This theory arises as a formal large-speed-of-light limit of the teleparallel equivalent of general relativity (TEGR). Thus, it provides a geometric formulation of the Newtonian limit of TEGR, similar to standard Newton--Cartan gravity being the Newtonian limit of general relativity. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered.
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Affine connections for Galilean and Carrollian structures: a unified perspective
The authors classify general Carrollian affine connections with torsion and non-metricity, show their emergence from Lorentzian limits, and build an ultra-relativistic geometric trinity of gravity theories.