Circular orbits around gravitating configurations of phantom scalar fields

In this work we consider general properties of circular orbits in the neighborhood of spherically symmetric static configurations of gravitating phantom scalar fields. In this case the metric area function $C(r)$ (in the quasiglobal coordinates) completely determines the type of a configuration (black hole, naked singularity, wormhole). In any of these cases stable circular orbits can exist only in the region $r\geqslant 3m,\, r\geqslant r_0$, where $r_0$ is a unique minimum point of the function $C(r)$, and $m$ is the mass of the configuration. Wormholes that are symmetric relative to the throat, and topological geons can have circular orbits only on their throats or on the corresponding topological surfaces; at that, possible values of specific angular momentums on the corresponding stable orbits are bounded from above. We also present a classification of the gravitating configurations according to type of their innermost stable circular orbits.