paper

On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field

arXiv:1111.2224 · doi:10.1016/j.physletb.2011.12.044

Abstract

We studied the low energy motion of particles in the general covariant version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Horava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton's gravity law even in the weak gravitational field approximation.

New result about equivalence principle added, improved discussion and typos corrected. Version to appear in Phys. Lett. B

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