标量场内禀引力扰动对裸奇点的影响
Interior gravitational perturbations to naked singularities of a scalar field
- Sun Yat-sen University（中山大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构造了Einstein-标量场裸奇点解的内禀引力扰动，在阈值Hölder正则性下保持大而有限，低于阈值时收敛到零，并将球对称结果推广到非球对称及局部化情形。
AI中文摘要：
针对Christodoulou构造的Einstein-标量场方程$k$-自相似裸奇点解，我们构造了一族导致陷获面形成的内禀引力扰动。这些扰动在阈值Hölder正则性下保持大但有限，而在低于阈值的所有正则性下收敛到零。这将在\cite{Li25}中低于阈值的球对称内禀结果推广到非球对称情形。我们进一步构造了一族真正局部化的扰动，其角向支撑收缩到单点，在该点之外光滑收敛到零。这利用了球对称之外额外的角向自由度。此外，当改用Sobolev正则性度量时，这类真正局部化的扰动族仍在低于同一阈值的所有正则性下收敛到零。
英文摘要：
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.
