  Possible astrophysical consequences of the Ho\v{r}ava quantum gravity theory
have been recently studied by several authors. They usually employ the
Kehagias-Sfetsos (KS) spacetime which is a spherically symmetric vacuum
solution of a specific version of Ho\v{r}ava's gravity. The KS metric has
several unusual geometrical properties that in the present article we examine
by means of the often used technique of embedding diagrams. We pay particular
attention to the transition between naked singularity and black-hole states,
which is possible along some particular sequences of the KS metrics.
