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arXiv · 1111.2224

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

Elcio Abdalla·Alan M. da Silva
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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.

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Elcio Abdalla, Alan M. da Silva. 2011-11-09. On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field. https://doi.org/10.1016/j.physletb.2011.12.044

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