波动坐标系下Einstein-非线性电磁系统Minkowski时空解的全局稳定性
The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates
摘要：
本文研究了广义相对论爱因斯坦场方程与一类非线性电磁场模型的耦合问题。该系列包括所有满足以下标准的协变电磁模型：它们可以从足够规则的拉格朗日导出，它们在弱场极限下简化为线性麦克斯韦模型，并且它们对应的能量动量张量满足主导能量条件。我们的主要结果是证明了耦合系统的1 + 3维Minkowski时空解对于包括线性Maxwell模型在内的任何成员都是全局非线性稳定的。这个稳定性的结果是一个小数据的整体存在性结果的减少方程组，相当于原来的系统在我们的波坐标规范。我们的时空度量分量的分析是基于最近开发的Lindblad和Rodnianski，这使我们能够得到适当的估计张量系统的准线性波方程的非线性，满足弱零条件的框架。我们的分析的电磁场，满足准线性一阶方程，是基于Christodoulou开发的几何能量方法框架的扩展，以及在文章中开发的法拉第张量的逐点衰减估计的集合。我们直接与电磁场一起工作，从而避免使用电磁势。
英文摘要：
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following criteria: they are derivable from a sufficiently regular Lagrangian, they reduce to the linear Maxwell model in the weak-field limit, and their corresponding energy-momentum tensors satisfy the dominant energy condition. Our main result is a proof of the global nonlinear stability of the 1 + 3-dimensional Minkowski spacetime solution to the coupled system for any member of the family, which includes the linear Maxwell model. This stability result is a consequence of a small-data global existence result for a reduced system of equations that is equivalent to the original system in our wave coordinate gauge. Our analysis of the spacetime metric components is based on a framework recently developed by Lindblad and Rodnianski, which allows us to derive suitable estimates for tensorial systems of quasilinear wave equations with nonlinearities that satisfy the weak null condition. Our analysis of the electromagnetic fields, which satisfy quasilinear first-order equations, is based on an extension of a geometric energy-method framework developed by Christodoulou, together with a collection of pointwise decay estimates for the Faraday tensor developed in the article. We work directly with the electromagnetic fields, and thus avoid the use of electromagnetic potentials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
