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

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

2009-10-25

arxiv.org/abs/0910.4776v1

Phys.Lett.B680:98-103,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

10.1016/j.physletb.2009.08.024

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 Schr\"odinger equations for the fluctuation field. An advantage of this approach over the usual $(3+1)$-dimensional General Relativity is that it allows us 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 Schr\"odinger equations.

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