Charge and Antipodal Matching across Spatial Infinity

TL;DR

This paper establishes a precise correspondence between data at null and spatial infinity, demonstrating the equivalence of soft graviton theorems and BMS charge conservation through antipodal matching relations.

Contribution

It provides a detailed map between Bondi data at null infinity and Beig-Schmidt data at spatial infinity, clarifying the relation between different BMS charge proposals.

Findings

Derived antipodal matching relations for gravitational scattering.

Mapped Bondi data to Beig-Schmidt data at spatial infinity.

Connected various BMS charge proposals with conserved charges at spatial infinity.

Abstract

We derive the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end we provide a precise map between Bondi data at null infinity $\mathscr{I}$ and Beig-Schmidt data at spatial infinity $i^0$ in a context appropriate to the gravitational scattering problem and celestial holography. In addition, we explicitly match the various proposals of BMS charges at $\mathscr{I}$ found in the literature with the conserved charges at $i^0$.