Naked Singularity Censoring with Anisotropic Apparent Horizon

TL;DR

This paper demonstrates that tiny anisotropic perturbations in initial data can lead to the formation of apparent horizons, effectively censoring naked singularities in the Einstein-scalar field system, advancing understanding of cosmic censorship.

Contribution

It introduces a novel approach that shows how small anisotropic perturbations can prevent naked singularities, using improved hyperbolic methods and new elliptic techniques.

Findings

Anisotropic perturbations lead to apparent horizon formation.

Naked singularities can be censored by small anisotropic perturbations.

Advances in hyperbolic and elliptic methods for Einstein-scalar systems.

Abstract

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 [18]. 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 $C^0$ 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.