SELF-SIMILAR COLLAPSE OF FLAT SYSTEMS

In response to the widespread distribution of sheets of galaxies in th e Universe we present self-similar solutions for the problem of the co llapse of axisymmetric, flat distributions of matter in Newtonian grav ity. All systems are self-gravitating and have infinite mass. A semi-a nalytic approach for solving the equations of motion is used, and the asymptotic limits of the solutions are tabulated. As the central regio n 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-simila r 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. When the point mass of the solution is made bigger, the s ystem first expands, then turns around and recollapses at the origin. In Appendix A, we give the solutions for the similar problem of a plan ar distribution of 'rods' collapsing into a line.