Nonspherical perturbations of critical collapse and cosmic censorship

TL;DR

This paper investigates how nonspherical perturbations affect critical gravitational collapse, showing that naked singularities remain of codimension one in the full phase space for perfect fluids with specific equations of state.

Contribution

It extends previous spherical symmetry results by demonstrating that naked singularities are robust under nonspherical perturbations in the phase space.

Findings

Naked singularities have codimension one in the full phase space near spherical symmetry.

Perturbations around spherical symmetry do not eliminate the critical behavior.

Results support the stability of naked singularities under nonspherical perturbations.

Abstract

Choptuik has demonstrated that naked singularities can arise in gravitational collapse from smooth, asymptotically flat initial data, and that such data have codimension one in spherical symmetry. Here we show, for perfect fluid matter with equation of state $p=\rho/3$, by perturbing around spherical symmetry, that such data have in fact codimension one in the full phase space, at least in a neighborhood of spherically symmetric data.