标题： 关于广义相对论中孤立系统的质心与常时空平均曲率曲面的叶状结构 显示英文标题

标题： On center of mass and foliations by constant spacetime mean curvature surfaces for isolated systems in General Relativity

摘要： 我们提出了一种新的渐近欧几里得初始数据集的叶状结构，由常时空平均曲率（STCMC）的2维球面组成。无论叶状结构是在哪个初始数据集中构造的，其叶子都具有STCMC性质，这表明在任意渐近平坦时空的空间无穷远处的邻域内存在大量STCMC 2维球面。STCMC叶状结构可以被视为Huisken和Yau建议的CMC叶状结构的一个协变相对论推广。我们证明了，在任何非零能量的渐近欧几里得初始数据集的无穷远处，存在唯一的STCMC叶状结构，这使得定义孤立系统的新的总质心成为可能。这个STCMC质心在环境时空的渐近庞加莱群的作用下表现出等变性，并且在爱因斯坦演化方程下像特殊相对论中的点粒子一样演化。新定义还修正了Huisken和Yau提出的定义孤立系统总质心的CMC方法中存在的微妙缺陷，这些缺陷被Cederbaum和Nerz描述过。 显示英文摘要

摘要： We propose a new foliation of asymptotically Euclidean initial data sets by 2-spheres of constant spacetime mean curvature (STCMC). The leaves of the foliation have the STCMC-property regardless of the initial data set in which the foliation is constructed which asserts that there is a plethora of STCMC 2-spheres in a neighborhood of spatial infinity of any asymptotically flat spacetime. The STCMC-foliation can be understood as a covariant relativistic generalization of the CMC-foliation suggested by Huisken and Yau. We show that a unique STCMC-foliation exists near infinity of any asymptotically Euclidean initial data set with non-vanishing energy which allows for the definition of a new notion of total center of mass for isolated systems. This STCMC-center of mass transforms equivariantly under the asymptotic Poincar\'e group of the ambient spacetime and in particular evolves under the Einstein evolution equations like a point particle in Special Relativity. The new definition also remedies subtle deficiencies in the CMC-approach to defining the total center of mass suggested by Huisken and Yau which were described by Cederbaum and Nerz.