Spherically symmetric solutions in Hořava-Lifshitz gravity and their properties

Nonprojectable Hořava 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 space-time 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 $g^2(r)$.

Figure 1

In this figure we plot $f_{\min }^{*}$, $f_{\max }^{*}$, and $f_0^{*}$ with $\tilde{r}=r/M$ and $\tilde{\omega }=\omega M^2=100$.