  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.
