Anisotropic fluid spheres in Horava gravity and Einstein-tether theory with a nonstatic tether

In this paper we consider spherically symmetric interior spacetimes tilled by anisotropic fluids in the context of Horava gravity and Einstein-ether theory. We assume a specific nonstatic configuration of the ether vector field and show that the field equations admit a family of exact analytical solutions which can he 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.