Spherical Symmetric Solutions in Ho\v{r}ava-Lifshitz Gravity and their Properties

Non-projectable Ho\v{r}ava gravity for a spherically symmetric configuration with $\lambda =1$ exhibits an infinite set of solutions parametrized by a generic function $g^2(r)$ for the radial component of the shift vector. In the IR limit the infinite set of solutions corresponds to the invariance of General Relativity under a spacetime reparametrization. In general, not being a coordinate transformation, the symmetry in the action responsible for the infinite set of solutions does not have a clear physical interpretation. Indeed it is broken by the matter term in the action. We study the behavior of the solutions for generic values of the parameter $g^2(r)$.