Naked singularities persist under non-spherically symmetric perturbations of Christodoulou's self-similar solution, but the inner Cauchy horizon is singular and inextendible.
The formation of black holes and singularities in spherically symmetric gravitational collapse.Communications on Pure and Applied Mathematics, 44(3):339–373, 1991
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Naked Singularities beyond Spherical Symmetry: Singular Inner Cauchy Horizons for the Einstein-Scalar Field System
Naked singularities persist under non-spherically symmetric perturbations of Christodoulou's self-similar solution, but the inner Cauchy horizon is singular and inextendible.