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Opposite charged two-body system of identical counter-rotating black holes

A 4-parametric exact solution describing a two-body system of identical Kerr-Newman counter-rotating black holes endowed with opposite electric/magnetic charges is presented. The axis conditions are solved in order to really describe two black holes separated by a massless strut. Moreover, the explicit form of the horizon half length parameter sigma in terms of physical Komar parameters, i.e., the Komar mass M, electric charge QE, angular momentum J, and a coordinate distance R is derived. Additionally, magnetic charges QB arise from the rotation of electrically charged black holes. As a consequence, in order to account for the contribution to the mass of the magnetic charge, the usual Smarr mass formula should be generalized, as it is proposed by A. Tomimatsu, Prog. Theor. Phys. 72, 73 (1984).