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Exact solution for two unequal counter-rotating black holes

The complete solution for two unequal counter-rotating black holes separated by a massless strut, is developed in terms of four arbitrary parameters involving two quantities σ1 and σ2 as the half length of the two rods representing the black hole horizons, the total mass M and the relative distance R between the centers of the horizons. A further attempt for describing the explicit form of this solution in terms of the physical parameters: The two Komar masses M1 and M2, Komar angular momenta per unit mass a1 and a2 (a1 and a2 have opposite sign), and the coordinate distance R, guided us to a 4-parameter subclass in which the five physical parameters satisfy a simple algebraic relation and the interaction force in this scheme looks like Schwarzschild type.