Interior gravitational perturbations to naked singularities of a scalar field
Abstract
For the k-self-similar naked singularity solutions of Einstein--scalar field equations constructed by Christodoulou, we construct a family of interior gravitational perturbations leading to trapped surface formation that remain large but finite at the threshold Hölder regularity, while converging to zero in all regularities below the threshold. This extends the interior spherically symmetric result below the threshold in \cite{Li25} to non-spherically symmetric setting. We further construct a genuinely localized family of perturbations whose angular support shrinks to a single point, with smooth convergence to zero away from that point. This exploits the additional angular freedom available beyond spherical symmetry. Moreover, when measured instead in Sobolev regularity, such genuinely localized family of perturbations still converges to zero in all regularities below the same threshold.
Related
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- A construction of charged naked singularities for the Einstein--Maxwell-charged scalar field equations in 3+1 dimensions
- Naked Singularities beyond Spherical Symmetry: Instability of κ-Self-Similar Solutions via an Iteration Scheme
- Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
- Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides
BibTeX
@misc{li2026interior,
title = {{Interior gravitational perturbations to naked singularities of a scalar field}},
author = {Junbin Li and Tingting Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15107},
eprint = {2609.15107},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15107},
}
RIS
TY - UNPB
TI - Interior gravitational perturbations to naked singularities of a scalar field
AU - Junbin Li
AU - Tingting Li
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15107
UR - https://arxiv.org/abs/2609.15107
AB - For the k-self-similar naked singularity solutions of Einstein--scalar field equations constructed by Christodoulou, we construct a family of interior gravitational perturbations leading to trapped surface formation that remain large but finite at the threshold Hölder regularity, while converging to zero in all regularities below the threshold. This extends the interior spherically symmetric result below the threshold in \cite{Li25} to non-spherically symmetric setting. We further construct a genuinely localized family of perturbations whose angular support shrinks to a single point, with smooth convergence to zero away from that point. This exploits the additional angular freedom available beyond spherical symmetry. Moreover, when measured instead in Sobolev regularity, such genuinely localized family of perturbations still converges to zero in all regularities below the same threshold.
ER -