Weak and strong field approximations and circular orbits of Kehagias-Sfetsos space-time

The Kehagias-Sfetsos asymptotically flat black hole and naked singularity solutions of Ho\v{r}ava-Lifshitz gravity are investigated both in the weak-field and strong-field regimes. In the weak-field limit the gravitational field generated by the Kehagias-Sfetsos spherically symmetric solution is weaker then in the case of the Schwarzschild black hole of general relativity. In the strong-field regime naked singularities with $\omega_{0} \ll 1 $ display an unusual distance dependence: gravity becomes weaker when approaching the singularity. The stability of circular orbits is also analyzed. While in the black hole case the square of the angular momentum should be larger than a certain finite, non-zero minimal value, in the naked singularity case there are stable circular orbits for any non-zero value of the angular momentum. In this regime we prove the existence of an infimum of the allowed radii of circular orbits (corresponding to vanishing angular momentum).