Self-similarity and Criticality in Gravitational Collapse

Abstract

We examine here the question whether self-similarity always implies criticality in gravitational collapse. To this end, we consider one-parameter families of self-similar collapse models, namely the collapse of radiation shells as given by the Vaidya metric and inhomogeneous dust collapse. The regions of parameter space which give rise to the collapse final states as black holes or naked singularity are evaluated to conclude that a non-zero measure set of values give rise to each of these final states. This scenario suggests the possibility that while a zero measure of solutions may admit a visible singularity in collapse calculations such as the numerical simulation of one-parameter family of massless scalar fields, some other collapse models need not behave in the same manner even when the collapse is self-similar. In other words, self-similarity does not imply a zero measure of naked singularity solutions necessarily for all collapse models in general. We also make some remarks here on perfect fluid collapse, and implications on the genericity and stability aspects of collapse outcomes are discussed.