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On any asymptotically-flat spacetime, we show that the asymptotic symmetriesand charges of Maxwell fields on past null infinity can be related to those onfuture null infinity as recently proposed by Strominger. We extend thecovariant formalism of Ashtekar and Hansen by constructing a 3-manifold of bothnull and spatial directions of approach to spatial infinity. This allows us tosystematically impose appropriate regularity conditions on the Maxwell fieldsnear spatial infinity along null directions. The Maxwell equations on this3-manifold and the regularity conditions imply that the relevant fieldquantities on past null infinity are antipodally matched to those on futurenull infinity. Imposing the condition that in a scattering process the totalflux of charges through spatial infinity vanishes, we isolate the subalgebra oftotally fluxless symmetries near spatial infinity. This subalgebra provides anatural isomorphism between the asymptotic symmetry algebras on past and futurenull infinity, such that the corresponding charges are equal near spatialinfinity. This proves that the flux of charges is conserved from past to futurenull infinity in a classical scattering process of Maxwell fields. We alsocomment on possible extensions of our method to scattering in generalrelativity.

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