  We propose an explanation of features of spiral galaxies: spiral arms and
observed flat rotation curves, without the presence of an exotic form of
matter. The formalism is based on Boltzmanns transport equation for the
collisional matter and the very-low-velocity post-Newtonian approximation of
the general relativity equations expressed in the Maxwell-like form. The
Maxwell-like formulation provides the base for the explanation of the above
phenomena in the language of dynamically created gravitoelectromagnetic fields
by the movement of mass streams in the plane of the galaxy disc. In the model
we use radical simplifications expressed as neglect of the gravitational
interaction between neighbors and approximation of the incompressible mass
flow. In this frame we show that if the galaxy disc is fuelled constantly by
collisional mass carriers, then the amplification of the gravitomagnetic field
can be large enough to create the rotational velocity pattern and spiral arms.
In this framework the collisional part of the mass gas in the galaxy disc
plane, i.e. molecules and atoms, is responsible for the creation of the
gravitomagnetic field. According to the model the spiral pattern of arms is
static and determined by a direction of the mass flow. The model reproduces
qualitatively the observed spiral arms and reproduces well the shape of the
rotational velocity pattern. As an example of the usability of the proposed
mechanism, we reproduce qualitatively the above features for the IC 342 and NGC
4321 galaxies.
