Convergent Null Data Expansions at Space-Like Infinity of Stationary Vacuum Solutions
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We present a characterization of the asymptotics of all asymptotically flat, stationary solutions with non-vanishing ADM mass to Einstein’s vacuum field equations. This characterization is given in terms of two sequences of symmetric trace free tensors (we call them the ‘null data’), which determine a formal expansion of the solution, and which are in a one to one correspondence to Hansen’s multipoles. We obtain necessary and sufficient growth estimates on the null data to define an absolutely convergent series in a neighborhood of spatial infinity. This provides a complete characterization of all asymptotically flat, stationary vacuum solutions to the field equations with non-vanishing ADM mass.