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

Physics – High Energy Physics – High Energy Physics - Theory

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

Scientific paper

10.1016/j.physletb.2011.12.044

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.

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