General static spherically symmetric solutions in Hořava gravity

We derive the equations describing a general static spherically symmetric configuration for the softly broken Hořava gravity introduced by A. Kehagias and K. Sfetsos with nonzero shift field and no-projectability condition. These represent “hedgehog” versions of black holes with radial “hair” arising from the shift field. For the case of the standard de Witt kinetic term ($\lambda =1$) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point $\lambda =\frac{1}{3}$. Moreover we obtain an implicit general expression for the solutions with $N_r=0$ and generic $\lambda$. In this context we study the presence of horizons for standard matter and the related Hawking temperature, generalizing the corresponding relations in the usual static spherically symmetric case.