论文标题
时空谐波函数和爱因斯坦方程的3维渐近初始数据的质量
Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations
论文作者
论文摘要
我们为爱因斯坦方程的三维渐近初始数据集的ADM能量摩托载体（ADM质量）的Lorentz长度提供了下限。除了物质场的能量密度之外，该结合是根据线性生长“时空谐波函数”给出的，无论主要能量条件是否存在或数据是否具有边界，都有效。该结果的必然是为完整的初始数据或具有弱捕获的表面边界的时空正理定理的新证明，并且包括刚性陈述，该刚度声明质量在且仅当数据来自Minkowski空间时就会消失。证明与Witten Spinorial方法以及Eichmair，Huang，Lee和Schoen的边缘外部捕获的表面（MOTS）的表面有一些类比。此外，本文概括了Bray，Stern和第二和第三作者的Riemannian Case中使用的谐波级集技术，尽管具有不同的水平集。因此，即使在时间对称（Riemannian）情况下，也达到了新的不等式。
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic functions' in addition to the energy-momentum density of matter fields, and is valid regardless of whether the dominant energy condition holds or whether the data possess a boundary. A corollary of this result is a new proof of the spacetime positive mass theorem for complete initial data or those with weakly trapped surface boundary, and includes the rigidity statement which asserts that the mass vanishes if and only if the data arise from Minkowski space. The proof has some analogy with both the Witten spinorial approach as well as the marginally outer trapped surface (MOTS) method of Eichmair, Huang, Lee, and Schoen. Furthermore, this paper generalizes the harmonic level set technique used in the Riemannian case by Bray, Stern, and the second and third authors, albeit with a different class of level sets. Thus, even in the time-symmetric (Riemannian) case a new inequality is achieved.
