Stationar spherical-symmetric configuration of dark matter

Abstract

The article is devoted to the consideration of a model problem, where mass flow of dark matter which take
as only gravitational interacting spherical continuous medium without pressure and with radial opposite
motion with equilibrium ascending and descending components, starting free fall from boundary of the
sphere and passing through the center, stopping and fall back at the boundary of the spherical mass
distribution, which give us stationary spherical-symmetric configuration of dark matter. The presence of an
opposite motion makes the configuration we are considering stationary. Limited mass and dimensions of
the dark matter distribution gives us possibility to modelling galaxy galo and dark stars. This configuration
is considered in the classical gravity. As a result of the study, we obtained a singular density distribution in
the center and in the shell of sphere and corresponding velocity field with singular center. The resulting
profile can be used to construct arbitrary distributions, corresponding to the observed profiles.