Conservation of asymptotic charges from past to future null infinity: Maxwell fields

TL;DR

This paper demonstrates that in Maxwell fields on asymptotically-flat spacetimes, the asymptotic charges at past and future null infinity are conserved through a systematic analysis involving a 3-manifold approach and regularity conditions, confirming flux conservation.

Contribution

It extends the covariant formalism to relate asymptotic charges at past and future null infinity, establishing charge conservation in Maxwell field scattering.

Findings

Asymptotic charges are antipodally matched at past and future null infinity.

Flux of charges is conserved in classical Maxwell scattering.

Subalgebra of fluxless symmetries provides an isomorphism between past and future charges.

Abstract

On any asymptotically-flat spacetime, we show that the asymptotic symmetries and charges of Maxwell fields on past null infinity can be related to those on future null infinity as recently proposed by Strominger. We extend the covariant formalism of Ashtekar and Hansen by constructing a 3-manifold of both null and spatial directions of approach to spatial infinity. This allows us to systematically impose appropriate regularity conditions on the Maxwell fields near spatial infinity along null directions. The Maxwell equations on this 3-manifold and the regularity conditions imply that the relevant field quantities on past null infinity are antipodally matched to those on future null infinity. Imposing the condition that in a scattering process the total flux of charges through spatial infinity vanishes, we isolate the subalgebra of totally fluxless symmetries near spatial infinity. This subalgebra provides a natural isomorphism between the asymptotic symmetry algebras on past and future null infinity, such that the corresponding charges are equal near spatial infinity. This proves that the flux of charges is conserved from past to future null infinity in a classical scattering process of Maxwell fields. We also comment on possible extensions of our method to scattering in general relativity.