Dark matter structures and emission of very long gravitational waves

Abstract

Formation of large structure in the Universe as a result of gravitational instability in cold dark matter is investigated in a simple analytical model. 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 uniform Maclaurin spheroid. Development of gravitational instability and collapse in tlie dark matter medium do not lead to any shock formation or radiation, but is characterized by non-colliskmal 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. A very long gravitational wave emission during the collapse is estimated, and their possible connection with the observed gravitational lenses is discussed.