General theory of Galilean gravity

Understand

We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large $c$ limit of the vielbein formulation of General Relativity.

• Milne boosts originate from local Lorentzian transformations, and the special cases of torsionless and twistless torsional geometries are explained in the context of the larger locally Lorentzian theory.
• We write the action for Newton-Cartan fields in the first order Palatini formalism, and the large $c$ limit of the Einstein equations.
• Finally, we obtain the generalised Eisenhart-Duval lift of the metric that plays an important role in non-relativistic holography.