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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.
We provide an exact mapping between the Galilian gauge theory, recently advocated by us cite{BMM1, BMM2, BM}, and the Poincare gauge theory. Applying this correspondence we provide a vielbein approach to the geometric formulation of Newtons gravity w
We consider a static self-gravitating perfect fluid system in Lovelock gravity theory. For a spacial region on the hypersurface orthogonal to static Killing vector, by the Tolmans law of temperature, the assumption of a fixed total particle number in
We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffats Modified theory of Gravity(MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency be
We investigate inflation and its scalar perturbation driven by a massive scalar field in the unimodular theory of gravity. We introduce a parameter $xi$ with which the theory is invariant under general unimodular coordinate transformations. When the
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action principle