  We study the geodesic structure of the Korkina-Grigoryev spacetime. The
corresponding metric is a generalization of the Schwarzschild geometry to the
case involving a massless scalar field. We investigate the relation between the
angular momentum of the test particle and the charge of the field, which
determines the shape of the effective-potential curves. The ratio for angular
momentum of the particle, the charge of the scalar field and the dimensionless
spatial parameter is found, under which the finite motion of particles occurs.
From the behavior of the potential curves the radii of both stable and unstable
circular orbits around a black hole are found, as well as the corresponding
energies of the test particles. The effective-potential curves for the
Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are
compared. It is shown, that in the case of the Korkina-Grigoryev metric the
stable orbits eventually vanish with increasing charge.
