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.
On the geometric trinity of gravity, non-relativistic limits, and Maxwell gravitation
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abstract
We show that the dynamical common core of the recently-discovered non-relativistic geometric trinity of gravity is Maxwell gravitation. Moreover, we explain why no analogous distinct dynamical common core exists in the case of the better-known relativistic geometric trinity of gravity.
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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.