  We give a new definition, based on considerations of well-posedness for a
certain asymptotic initial value problem, of the phase space for the radiative
degrees of freedom of the gravitational field in exact General Relativity. This
space fibres over the space of final states, with the fibres being the purely
radiative degrees of freedom. The symplectic form is rigorously identified.
  The infrared sectors are shown to be the level surfaces of a moment map of an
action of the quotient group Supertranslations/Translations. A similar result
holds for Electromagnetism in Minkowski space.
