A 4-parametric exact solution describing a two-body system of identical Kerr-Newman counterrotating 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 σ in terms of physical Komar parameters, i.e., Komar's 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).

A 5-parametric exact solution, describing a binary system composed of identical counter-rotating black holes endowed with opposite electromagnetic charges, is constructed. The addition of the angular momentum parameter to the static Emparan-Teo dihole model introduces magnetic charges into this two-body system. The solution can be considered as an extended model for describing generalized black diholes as dyons. We derive the explicit functional form of the horizon half-length parameter $\sigma$ as a function of the Komar parameters: Komar mass $M$, electric/magnetic charge $Q_{E }/ Q_{B}$, angular momentum $J$, and a coordinate distance $R$, where the parameters $(M, J, Q_E, Q_B, R)$ characterize the upper constituent of the system, while $(M, -J, -Q_E, -Q_B, R)$ are associated with the lower one. The addition of magnetic charges enhances the standard Smarr mass formula in order to take into account their contribution to the mass. The solution contains, as particular cases, two solutions already discussed in the literature.Comment: 8 pages, 3 figures, 1 table; accepted in Phys. Rev.

A binary system of identical corotating Kerr sources is studied after deriving the corresponding 3-parametric asymptotically flat exact solution. Both sources are apart from each other by means of a massless strut (conical singularity). In the context of black holes, the analytical functional form of each horizon {\sigma} is expressed in terms of arbitrary Komar physical parameters: mass M, angular momentum J (with parallel spin), and the coordinate distance R between the center of each horizon. Later on, all the thermodynamical properties related to the horizon are depicted by concise formulae. Finally, the extreme limit case is obtained as a 2-parametric subclass of Kinnersley-Chitre metric.Comment: 7 pages, 7 figures, improved figures, typos correcte

A complete solution describing a binary system constituted by two unequal counter-rotating black holes with a massless strut in between is presented. It is expressed in terms of four arbitrary parameters: the half length of the two rods representing the black hole horizons σ1 and σ2, the total mass M and the relative distance R between the centers of the horizons. The explicit parametrization of this solution in terms of physical parameters, i.e., the Komar masses M1 and M2, the Komar angular momenta J1 and J2 (having J1 and J2 opposite signs) and the coordinate distance R, led us to a 4-parameter subclass in which the five physical parameters satisfy a simple algebraic relation, which generalizes the two statements made by Bonnor, in order to remove the additional contributions from the massless spinning rods outside the black holes. Moreover, the interaction force turns out to be of the same form as in the double-Schwarzschild static case.