Contributor info: Dr Kevin Nguyen

Geoffrey Compère, Dima Fontaine, Kevin Nguyen

SciPost Phys. Core 8, 066 (2025) · published 10 October 2025 | Toggle abstract · pdf

We study the general structure of the electromagnetic field in the vicinity of spatial infinity. Starting from the general solution of the sourced Maxwell equations written in terms of multipole moments as obtained by Iyer and Damour, we derive the expansion of the electromagnetic field perturbatively in the electromagnetic coupling. At leading order, where the effect of long-range Coulombic interactions between charged particles is neglected, we discover infinite sets of antipodal matching relations satisfied by the electromagnetic field, which extend and sometimes correct previously known relations. At next-to-leading order, electromagnetic tails resulting from these Coulombic interactions appear, which affect the antipodal matching relations beyond those equivalent to the leading soft photon theorem. Moreover, new antipodal matching relations arise, which we use to re-derive the classical logarithmic soft photon theorem of Sahoo and Sen. Our analysis largely builds upon that of Campiglia and Laddha, although it invalidates the antipodal matching relation which they originally used in their derivation. The antipodal matching relations and the proof of the classical logarithmic soft photon theorem agree with an earlier analysis of Bhatkar, which we generalize using other methods.

Federico Capone, Kevin Nguyen, Enrico Parisini

SciPost Phys. 14, 014 (2023) · published 6 February 2023 | Toggle abstract · pdf

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 $i^0$.