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

Abstract

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 and . 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 and a geometric identification of cuts of with points of Minkowski then produces an integral formula of Kirchhoff type. Finally, and 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 Poincaré 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.