On the analyticity of stationary gravitational fields at spatial infinity

It is proved that all stationary, vacuum solutions of Einstein’s equations which satisfy certain weak differentiability conditions characterizing asymptotic flatness, possess an analytic structure near spatial infinity. This analyticity theorem implies the existence of a multipole expansion whose coefficients can be expressed in terms of the Geroch–Hansen multipole moments defined at the point at infinity on the conformal manifold. This proves a longstanding conjecture that these moments uniquely determine the local structure of a stationary, asymptotically flat, vacuum metric.