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Exact solution for a binary system of unequal counter-rotating black holes

A complete solution describing a binary system constituted by two unequal counter-rotating black holes with a massless strut inbetween is presented. It is expressed in terms of four arbitrary parameters: the half length of the two rods representing the black hole horizons sigma1 and sigma2, the total mass M, and the relative distance R between the centers of the horizons. The explicit form of this solution in terms of physical parameters, i.e., the Komar masses M1 and M2, the Komar angular momenta per unit mass a1 and a2, having a1 and a2 opposite signs, and the coordinate distance R, led us to a 4-parameter subclass of solutions in which a set of five physical parameters satisfy a simple algebraic relation. Moreover, the interaction force, provided by the strut, between the black holes results to be of same form as it is for the static double-Schwarzschild case.