Interaction of two black holes in the slow-motion limit

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Abstract
The interaction of two black holes is considered under the assumptions that each black hole moves in the far field of the other and that the relative velocity is small compared to the speed of light; the black holes may rotate and possess comparable masses. A method of matched asymptotic expansions developed previously by the author is used to relate the gravitational field far from the black holes, described by a slow-motion perturbation of flat space, to the gravitational field near the holes, described by perturbations of the Kerr geometry. This leads to equations of motion and spin propagation giving the main deviations from Newtonian behavior. The derivation uses only the vacuum Einstein equations, and the resulting equations are generalizations of well-known expressions for the interaction of massive or rotating bodies in general relativity.