标题： 全局非线性稳定的大型数据解到爱因斯坦标量场系统 显示英文标题

标题： Global Non-Linearly Stable Large-Data Solutions to the Einstein Scalar Field System

摘要： 我研究了一类全局的、因果测地完备的球对称爱因斯坦标量场（SSESF）系统的解。 扩展了Luk-Oh（定量衰减率对于球对称爱因斯坦标量场系统的发散解，arXiv:1402.2984），Luk-Oh-Yang（具有大有界变分范数的球对称爱因斯坦标量场系统的解，arXiv:1605.03893）的结果，我提供了新的界限，用于控制SSESF系统的大数据解的度规分量和标量场本身的高阶导数。 此外，通过构造一个特定的广义波坐标集，我证明了，根据Luk和Oh的最新结果，在假设数据足够光滑的情况下，这些解对于非球对称扰动是全局非线性稳定的。 特别是，我展示了存在大量非平凡的例子，这些例子是大数据、全局非线性稳定且发散的爱因斯坦标量场系统的解。 显示英文摘要

摘要： I study a class of global, causal geodesically complete solutions to the spherically symmetric Einstein scalar field (SSESF) system . Extending results of Luk-Oh (Quantitative Decay Rates for Dispersive Solutions to the Einstein-Scalar Field System in Spherical Symmetry, arXiv:1402.2984), Luk-Oh-Yang (Solutions to the Einstein-Scalar-Field System in Spherical Symmetry with Large Bounded Variation Norms, arXiv:1605.03893), I provide new bounds controlling higher derivatives of both the metric components of the solution and the scalar field itself for large data solutions to SSESF. Moreover, by constructing a particular set of generalized wave-coordinates, I show that, assuming sufficient regularity of the data, these solutions are globally non-linearly stable to non-spherically symmetric perturbations by recent results of Luk and Oh. In particular, I demonstrate the existence of a large collection of non-trivial examples of large data, globally nonlinearly stable, dispersive solutions to the Einstein scalar field system.