Non-relativistic gravity theories in four spacetime dimensions

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 non-relativistic MacDowell-Mansouri gravity theory by considering a generalized Newton-Hooke algebra.

20 pages

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• Review on Non-Relativistic Gravity
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• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Three-dimensional non-relativistic Hietarinta supergravity
• Extended Bargmann FDA and non-relativistic gravity