标题： 爱因斯坦真空方程的多局域时间对称初始数据 显示英文标题

标题： Multi-localized time-symmetric initial data for the Einstein vacuum equations

摘要： 我们构建了一类时间对称的初始数据集，用于爱因斯坦真空方程，这些数据集模拟了多个“几乎孤立”系统的简单配置。 每个这样的初始数据集由若干局部引力辐射源组成，并位于一个数据集族中，该族在通过任意大的倍数缩放系统间距离时是封闭的。 此类数据集包含非渐近平坦的数据集，但仍然可以赋予它们有限的ADM质量。 该构造通过使用Brill--Lindquist度规作为模板进行粘合方案来实现。 此类初始数据部分是出于理解广义相对论背景下远距离系统动态相互作用的愿望而提出的。 作为构造的副产品，我们得到了具有平凡拓扑和无限多个极小球面的完整、标量平坦的初始数据，以及具有无限多个爱因斯坦--罗森桥的初始数据。 显示英文摘要

摘要： We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized sources of gravitational radiation, and lies in a family of data sets which is closed under scaling out the distances between the systems by arbitrarily large amounts. This class contains data sets which are not asymptotically flat, but to which nonetheless a finite ADM mass can be ascribed. The construction proceeds by a gluing scheme using the Brill--Lindquist metric as a template. Such initial data are motivated in part by a desire to understand the dynamical interaction of distant systems in the context of general relativity. As a by-product of the construction, we produce complete, scalar-flat initial data with trivial topology and infinitely many minimal spheres, as well as initial data with infinitely many Einstein--Rosen bridges.