A review of our results on the asymptotic structure of gravity at spatial infinity in four spacetime dimensions is given. Finiteness of the action and integrability of the asymptotic Lorentz boost generators are key criteria that we implement through appropriate boundary conditions. These conditions are “twisted parity conditions,” expressing that the leading order of the asymptotic fields obeys strict parity conditions under the sphere antipodal map up to an improper gauge transformation. The asymptotic symmetries are shown to form the infinite-dimensional Bondi-Metzner-Sachs group, which has a nontrivial action. The charges and their algebra are worked out. The presentation aims at being self-contained and at possessing a pedagogical component.

中文翻译：

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四个时空维度中空间无穷大处的重力渐近结构

在四个时空维度上，我们对空间无穷大的重力渐近结构的结果进行了回顾。渐近洛伦兹升压发生器的动作有限和可集成性是我们通过适当的边界条件实现的关键标准。这些条件是“扭曲奇偶条件”，表示渐近场的前导顺序在球对映体映射下直至不规范变换之前都遵循严格的奇偶条件。渐近对称性被显示为形成了无穷作用的无穷维Bondi-Metzner-Sachs群。算出电荷和它们的代数。该演示文稿旨在自成一体并具有教学法的组成部分。