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We propose an explanation of features of spiral galaxies: spiral arms andobserved flat rotation curves, without the presence of an exotic form ofmatter. The formalism is based on Boltzmanns transport equation for thecollisional matter and the very-low-velocity post-Newtonian approximation ofthe general relativity equations expressed in the Maxwell-like form. TheMaxwell-like formulation provides the base for the explanation of the abovephenomena in the language of dynamically created gravitoelectromagnetic fieldsby the movement of mass streams in the plane of the galaxy disc. In the modelwe use radical simplifications expressed as neglect of the gravitationalinteraction between neighbors and approximation of the incompressible massflow. In this frame we show that if the galaxy disc is fuelled constantly bycollisional mass carriers, then the amplification of the gravitomagnetic fieldcan 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 discplane, i.e. molecules and atoms, is responsible for the creation of thegravitomagnetic field. According to the model the spiral pattern of arms isstatic and determined by a direction of the mass flow. The model reproducesqualitatively the observed spiral arms and reproduces well the shape of therotational velocity pattern. As an example of the usability of the proposedmechanism, we reproduce qualitatively the above features for the IC 342 and NGC4321 galaxies.

Spiral Galaxies - classical description of spiral arms and rotational velocity pattern - toy model