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Naked singularity censoring with anisotropic apparent horizon
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DOI：10.4007/annals.2025.201.3.3.png)
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Abstract
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Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in 1994. We further investigate the censorship of Christodoulou's naked singularity and show that a tiny anisotropic perturbation arising from the outgoing characteristic initial data would lead to the emergence of an anisotropic apparent horizon, which covers and censors the naked singularity. Our approach advances the hyperbolic short-pulse method by not requiring the aid of additional large parameters, by permitting the use of initial perturbations for the shear tensor and the derivative of scalar field to be with finite BV and C0 norms, and by allowing the initial perturbation to be arbitrarily small in scale-critical norms. New elliptic arguments based on non-perturbative methods are also developed.
Keywords:
naked singularity
weak cosmic censorship
anisotropic apparent horizon
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