  The most general vacuum solution to Einstein's field equations with no
incoming radiation can be constructed perturbatively from two infinite sets of
canonical multipole moments, which are found to be mapped into each other under
gravitational electric-magnetic duality at the non-linear level. We demonstrate
that in non-radiative regions such spacetimes are completely characterized by a
set of conserved celestial charges that consist of the Geroch-Hansen multipole
moments, the generalized BMS charges and additional celestial multipoles
accounting for subleading memory effects. Transitions among non-radiative
regions, induced by radiative processes, are therefore labelled by celestial
charges, which are identified in terms of canonical multipole moments of the
linearized gravitational field. The dictionary between celestial charges and
canonical multipole moments allows to holographically reconstruct the metric in
de Donder, Newman-Unti or Bondi gauge outside of sources.
