A simplified model of the formation of structures in the dark matter, and a background of very long gravitational waves

Abstract

Collapse of the rotating spheroid is approximated by a system of ordinary differential equations describing its dynamics. The gravitational potential is approximated by the one of the iniform Maclaurin spheroid. Developement of gravitational instability and collapse in the dark matter medium do not lead to any shock formation or radiation, but is characterized by non-collisional relaxation, which is accompanied by the mass and angular momentum losses. Phenomenological account of these processes is done in this model. Formation of the equilibrium configuration dynamics of collapse is investigated for several parameters, characterizing the configuration. A very long gravitational wave emission during the collapse is estimated, and their possible connection with the observed gravitational lenses is discussed.