发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对爱因斯坦-标量场系统，引入新型迭代方案证明了球对称外κ-自相似裸奇点的非线性不稳定性，还确立了相关物质聚焦条件下边际外俘获面的存在性。
AI 中文摘要
本文针对爱因斯坦-标量场系统，在我们近期构造非球对称近似κ-自相似裸奇点解的工作基础上，开展了其不稳定性的对应研究。这些奇异解包含大量非球对称边界项，而要证明其不稳定性，文献[2]中开发的精细重整化程序无法推广到本文考虑的更奇异情形。为克服这些困难，我们引入了一种适用于奇异背景的新型迭代方案，该方案的主导阶几何依赖于角变量。在每一步迭代中，利用前一步的双零几何冻结非线性系数，并按三角顺序求解所得方程。通过这种方式，非球对称边界项被纳入近似几何，而非作为微扰误差处理，从而得到逐步更精确的估计。经过足够多次迭代后，该方案可控制奇异角结构，并生成一个近似时空，其与精确解的差异满足所需界值。这些界值尤其提供了足够大的存在区域，以开展不稳定性论证。我们进一步证明，出射数据的各向异性扰动在标度临界范数下任意小，都会导致俘获面的形成。我们还构建并验证了一种物质聚焦条件，在此条件下，抛物型流论证保证存在对应的边际外俘获面（MOTS）。这些结果共同确立了爱因斯坦-标量场系统中球对称之外κ-自相似裸奇点的非线性不稳定性，并为跨爱因斯坦系统的应用引入了一个框架。
英文摘要
This paper provides the instability counterpart to our recent construction of nonspherically symmetric approximating $κ$-self-similar naked-singularity solutions for the Einstein--scalar field system. These singular solutions contain pervasive nonspherical borderline terms, and to prove instability the delicate renormalization procedure developed in [2] does not extend to the more singular setting considered here. To overcome these difficulties, we introduce a new iteration scheme adapted to singular backgrounds whose leading-order geometry depends on the angular variables. At each step, the nonlinear coefficients are frozen using the preceding double-null geometry, and the resulting equations are solved in a triangular order. In this way, the nonspherical borderline terms are incorporated into the approximate geometry rather than treated as perturbative errors, yielding successively sharper estimates. After sufficiently many iterations, the scheme controls the singular angular structure and produces an approximate spacetime whose difference from the exact solution satisfies the required bounds. In particular, these bounds provide an existence region large enough to carry out the instability argument. We further prove that anisotropic perturbations of the outgoing data, arbitrarily small in a scale-critical norm, lead to the formation of a trapped surface. We also formulate and verify a matter-focusing condition under which a parabolic flow argument guarantees the existence of a corresponding marginally outer trapped surface (MOTS). Together, these results establish the nonlinear instability of $κ$-self-similar naked singularities beyond spherical symmetry in the Einstein--scalar field system and introduce a framework for applications across Einstein systems.
Comments51 pages
