Multipole expansion of stationary asymptotically flat vacuum metrics in general relativity

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Abstract
A multipole expansion scheme is introduced for a wide class of stationary, asymptotically flat, vacuum solutions of Einstein’s equations using the conformal techniques of Geroch and Hansen. An intrinsic choice of the conformal factor and suitable asymptotic flatness conditions enable one to express the rescaled gravitational mass and angular momentum potentials and the rescaled spatial metric as power series in normal coordinates around a point Λ representing the spatial infinity on the conformal manifold. The coefficients of this expansion are certain nonlinear combinations of the Hansen multipole moments. As an example the Schwarzschild metric is discussed in the present framework.