  We study a static spherically symmetric problem with a black hole and
radially directed geodesic flows of dark matter. The obtained solutions have
the following properties. At large distances, the gravitational field produces
constant velocities of circular motion, i.e., flat rotation curves. At smaller
distances, the field switches to Newtonian regime, then to Schwarzschild
regime. Deviations from Schwarzschild regime start below the gravitational
radius. The dark matter prevents the creation of event horizon, instead, a
spherical region possessing extremely large redshift is created. The structure
of space-time for the obtained solutions is investigated and the implications
for the models of the galaxies are discussed.
