Naked singularities and other features of self-similar general-relativistic gravitational collapse

Self-similar solutions are commonly used to describe Newtonian gravitational collapse. We examine, here, the structure of general-relativistic spherical collapse solutions for a perfect fluid with a barotropic equation of state. We find that these solutions are quite different from the homogeneous Oppenheimer-Snyder dust collapse solution on which our intuition is so heavily based. The most amazing feature that we find is the generic appearance of naked singularities in these solutions.