The self-similar evolution of holes in an Einstein-de Sitter universe

Similarity solutions have been found for the nonlinear evolution of spherical holes in an Einstein-de Sitter universe. A negative perturbation grows until it becomes a hole, which expands in a self-similar fashion, in most cases sweeping up and compressing the matter around it into a thin, dense shell. Holes compensated by an overdense shell are considered, and it is shown that the Einstein-de Sitter-Sedov solution for a cosmological blast wave gives the self-similar adiabatic flow of a collisional gas around such a hole. The corresponding solution for a collisionless gas is given, followed by a solution for a collisional gas with omega much less than one. Uncompensated holes are treated, giving solutions for a collisionless gas, a collisional gas, and for a mixture where the collisionless gas dominates. The possibility that holes may form naturally from the growth of fluctuations in a hierarchical clustering model is examined. Several processes modifying the similarity solutions are discussed.