  The non-gauge vector field with as simple as possible Lagrangian
(\ref{Lagrangian}) turned out an adequate tool for macroscopic description of
the main properties of dark matter. The dependence of the velocity of a star on
the radius of the orbit $V\left(r\right) $ -- galaxy rotation curve -- is
derived analytically from the first principles\ completely within the
Einstein's general relativity. The Milgrom's empirical modification of
Newtonian dynamics in nonrelativistic limit (MOND) gets justified and specified
in detail. In particular, the transition to a plateau is accompanied by damping
oscillations. In the scale of a galaxy, and in the scale of the whole universe,
the dark matter is described by a vector field with the same energy-momentum
tensor. It is the evidence of the common physical nature. Now, when we have the
general expression (\ref{Tik b=c=0}) for the energy-momentum tensor of dark
matter, it is possible to analyze its influence on the structure and evolution
of super heavy stars and black holes.
