General static spherically symmetric solutions in Hořava gravity

Abstract

We derive the equations describing a general static spherically symmetric configuration for the softly broken Ho\ifmmode \check{r}\else \v{r}\fi{}ava 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 ($\ensuremath{\lambda}=1$) 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 $\ensuremath{\lambda}=\frac{1}{3}$. Moreover we obtain an implicit general expression for the solutions with ${N}_{r}=0$ and generic $\ensuremath{\lambda}$. 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.