We study formal expansions of asymptotically flat solutions to the static
vacuum field equations which are determined by minimal sets of freely
specifyable data referred to as `null data'. These are given by sequences of
symmetric trace free tensors at space-like infinity of increasing order. They
are 1:1 related to the sequences of Geroch multipoles. Necessary and sufficient
growth estimates on the null data are obtained for the formal expansions to be
absolutely convergent. This provides a complete characterization of all
asymptotically flat solutions to the static vacuum field equations.Comment: 65 page
