Weak-field approximation of effective gravitational theory with local Galilean invariance

We examine the weak-field approximation of locally Galilean invariant gravitational theories with general covariance in a (4 + 1)-dimensional Galilean framework. The additional degrees of freedom allow us to obtain Poisson, diffusion, and Schrodinger equations for the fluctuation field. An advantage of this approach over the usual (3 + 1)-dimensional General Relativity is that it allows LIS to choose an ansatz for the fluctuation field that can accommodate the field equations of the Lagrangian approach to MOdified Newtonian Dynamics (MOND) known as AQUAdratic Lagrangian (AQUAL). We investigate a wave solution for the Schrodinger equations. (C) 2009 Elsevier B.V. All rights reserved.