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.