Nonspherical perturbations of critical collapse and cosmic censorship

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  • 12 October 1997
Abstract
Numerical simulations have shown that, in general relativity with various kinds of matter, initial data that form a naked singularity have codimension one within spherical symmetry. The singularity is approached through a self-similar spacetime which is the same for all initial data and even for universality classes of matter models. The codimension is one because this critical solution has precisely one perturbation mode that grows towards the singularity (and which must be suppressed by fine-tuning). Here we go beyond spherical symmetry. For a perfect fluid with equation of state p = (1/3) rho we construct the spherically symmetric critical solution and examine its linear perturbations, both spherical and non-spherical. We find only the one spherical growing mode already known, while all nonspherical modes decay. This means that naked singularities, for this matter model at least, have codimension one in a region of the space of initial data.

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