The BMS4 algebra at spatial infinity

TL;DR

The paper shows that a global BMS4 algebra naturally emerges from the asymptotic symmetry structure at spatial infinity under Compère–Dehouck conditions. Through linearised gravity and Friedrich’s conformal framework, it proves that this spatial-infinity algebra coincides with Strominger’s global BMS4 at null infinity, with antipodal matching of super-translation parameters and corresponding charges. The work connects spatial and null infinity through explicit charge identifications and provides a linearised bridge between infrared gravitational memory, soft theorems, and S-matrix symmetries. It also situates these results within prior electromagnetism analogues and hints at non-linear extensions and Hamiltonian formulations.

Abstract

We show how a global BMS4 algebra appears as the asymptotic symmetry algebra at spatial infinity. Using linearised theory, we then show that this global BMS4 algebra is the one introduced by Strominger as a symmetry of the S-matrix.