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We present a characterization of the asymptotics of all asymptotically flatstationary vacuum solutions of Einstein's field equations. Thischaracterization is given in terms of two sequences of symmetric trace freetensors (we call them the `null data'), which determine a formal expansion ofthe solution, and which are in a one to one correspondence to Hansen'smultipoles. We obtain necessary and sufficient growth estimates on the nulldata to define an absolutely convergent series in a neighbourhood of spatialinfinity. This provides a complete characterization of all asymptotically flatstationary vacuum solutions to the field equations.

Convergent null data expansions at space-like infinity of stationary vacuum solutions