Abstract:
A proof is given for the existence and uniqueness of a stationary vacuum solution (M,g,xi) of the boundary value problem consisting of Einstein's equations in an exterior domain M diffeomorphic to R x Sigma, where Sigma is the exterior of some ball in Euclidean 3-space, and boundary data depending on the Killing field xi on the boundary of Sigma. The boundary data must be sufficiently close to that of a stationary, spatially conformally flat vacuum solution (M, g_0, xi_0).
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