Abstract
We study some properties of a recently proposed local Lorentz-violating Finsler geometry, the so-called bipartite space. This anisotropic structure deforms the causal null surface to an elliptic cone and provides an anisotropy to the inertia. We obtain the new modified dispersion relations and the geodesic equation for a massive particle. For a weak directional-dependence we find the dynamical and interaction terms analogous to the gravitational sector of the Standard Model Extension.
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