Anisotropic fluid spheres in Ho\v{r}ava gravity and Einstein-\ae ther theory with a non-static \ae ther

Understand

In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Ho\v{r}ava gravity and Einstein-aether theory.

• We assume a specific non-static configuration of the aether 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.