AI 中文总结
该研究提出通过径向 boost 缩放，可从经典局部小数据存在性结果得到陷获面动力学形成结果，阐明短脉冲假设的几何光学本质，补充了爱因斯坦场方程陷获面形成的相关理论。
AI 中文摘要
Christodoulou、Klainerman、Rodnianski、Luk、An 等人的工作已给出爱因斯坦场方程真空解中陷获面动力学形成的若干结果。由于 Christodoulou 和 Klainerman 证明的闵可夫斯基时空稳定性意味着，爱因斯坦真空方程的“小”初始数据必然产生无奇异性的解，因此也无陷获面，故此前人们认为陷获面的动力学形成需要非线性双曲型爱因斯坦场方程的（困难）大数据存在性结果。本文与此相反，证明可通过一种称为径向 boost 的缩放，从经典的局部小数据存在性结果中得到与 Christodoulou 及 Klainerman-Rodnianski 结果在性质上相似的动力学陷获面形成结果。在此过程中，我们还阐明了短脉冲假设作为几何光学假设的本质，表明在该缩放图景中，所谓的入射剪切在最高阶满足线性波动方程。
英文摘要
Work of Christodoulou, Klainerman, Rodnianski, Luk, An, and others has provided a number of results on the dynamical formation of trapped surfaces in vacuum solutions to the Einstein field equations. Since the stability of Minkowski spacetime as proved by Christodoulou and Klainerman implies that `small' initial data to the Einstein vacuum equations must give rise to a solution with no singularities, and hence no trapped surfaces, it has been assumed that dynamical formation of trapped surfaces requires a (hard) large-data existence result for the nonlinear hyperbolic Einstein field equations. In this paper we show, to the contrary, that dynamical trapped surface formation results qualitatively similar to those of Christodoulou and Klainerman-Rodnianski can be obtained from (classical) local, small-data existence results via a scaling we term a radial boost. In the process we also fully elucidate the short-pulse ansatz as a geometric optics ansatz by showing that, in this scaled picture, the so-called incoming shear satisfies, at highest order, a linear wave equation.
Comments18 pages, 1 figure
