Anisotropic fluid spheres in Hořava gravity and Einstein-æther theory with a nonstatic æther

In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Hořava gravity and Einstein-æther theory. We assume a specific nonstatic configuration of the æther vector field and show that the field equations admit a family of exact analytical solutions which can be obtained if one of the two metric coefficients is assigned. We study as an illustrative example the case in which the metric of the interior spacetime reproduces the Newtonian potential of a fluid sphere with constant density.