Non-relativistic gravity theories in four spacetime dimensions

Shirt Abstract In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation.We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra.We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant.

Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field.We extend our results to a generalized 2006 nissan altima radio non-relativistic MacDowell-Mansouri gravity theory by considering a generalized Newton-Hooke algebra.