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

TL;DR

This paper introduces invariant extended boundary notions at timelike and spacelike infinity in asymptotically flat spacetimes, linking them to asymptotic symmetries and Carrollian geometries.

Contribution

It defines Ti and Spi boundaries from asymptotic metric data, demonstrating their relevance and symmetry properties, and connects them to scattering data and Carrollian structures.

Findings

Ti and Spi are invariant boundaries constructed from asymptotic data.

Automorphisms of Ti and Spi correspond to asymptotic symmetries.

Carrollian geometries reduce symmetry groups to BMS or Poincaré.

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 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.