The multipole structure of stationary space-times

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Abstract
A definition of multipole moments for stationary asymptotically flat solutions of Einstein’s equations is proposed. It is shown that these moments characterize a given space-time uniquely. Conversely, they can be arbitrarily prescribed, i.e., they generate power series for the field variables which satisfy the field equations to all orders. Despite their apparently rather different origin, they are shown to be identical with the Geroch–Hansen ones.

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