Self-similar collapse of flat systems

Abstract

In response to the widespread distribution of sheets of galaxies in the Universe we present self-similar solutions for the problem of the collapse of axisymmetric, flat distributions of matter in Newtonian gravity. All systems are self-gravitating and have infinite mass. A semi-analytic approach for solving the equations of motion is used, and the asymptotic limits of the solutions are tabulated. As the central region of the planar distribution converges to the origin, the length scale shrinks to zero, a point mass forms, and the solutions continue with a growing point mass dominating an enlarging region of the self-similar accretion flow. If time is reversed, this solution is interpreted as an exploding point mass: matter is scattered in a plane, and escapes to infinity