标题： Ti和Spi，类 Carroll 无限边界在类时和空间无限处 显示英文标题

标题： Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity

摘要： 本文的目标是提供一个关于时间与类空无限处扩展边界的定义，按照Figueroa-O'Farril--Have--Prohazka--Salzer的称呼，我们称之为Ti和Spi。 这个定义适用于Ashtekar--Romano意义上的渐近平直时空，并希望通过例子展示其在多种情况下的相关性。 该定义是不变的，仅从度量的渐近数据构造而成，并且扩展边界上的自同构可以与渐近对称性进行规范识别。 此外，质量场的散射数据被实现为Ti上的函数，而Ti截面与闵可夫斯基空间点的几何识别则产生了一个Kirchhoff类型的积分公式。 最后，Ti和Spi都自然地配备了（强）Carroll几何，在适度假设下，这使得对称群可以减少到BMS群，或在平坦情况下减少到Poincaré群。 特别是，Strominger的匹配条件通过限制到与Spi的离散对称性相容的Carroll几何自然实现。 显示英文摘要

摘要： The goal of this paper is to provide a definition for a notion of extended boundary at time and space-like infinity which, following Figueroa-O'Farril--Have--Prohazka--Salzer, we refer to as Ti and Spi. This definition applies to asymptotically flat spacetime in the sense of Ashtekar--Romano and we wish to demonstrate, by example, its pertinence in a number of situations. The definition is invariant, is constructed solely from the asymptotic data of the metric and is such that automorphisms of the extended boundaries are canonically identified with asymptotic symmetries. Furthermore, scattering data for massive fields are realised as functions on Ti and a geometric identification of cuts of Ti with points of Minkowksi then produces an integral formula of Kirchhoff type. Finally, Ti and Spi are both naturally equipped with (strong) Carrollian geometries which, under mild assumptions, enable to reduce the symmetry group down to the BMS group, or to Poincar\'e in the flat case. In particular, Strominger's matching conditions are naturally realised by restricting to Carrollian geometries compatible with a discrete symmetry of Spi.