Abstract
An exact asymptotically flat four-parameter solution of the Einstein-Maxwell equations representing the exterior field of two identical Kerr-Newman sources with angular momenta oppositely orientated is constructed in a simple analytical form. We show that there are no equilibrium states in such compact systems except for the case when the masses of the sources are equal to their charges. The condition for the existence of two horizons in the `antisymmetric' binary system turns out to be more stringent than in the case of a single Kerr-Newman black hole.
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