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

Understand

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.