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 \sigma 1 and \sigma 2 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algebraic relation and the interaction force in this scheme looks like Schwarzschild type.Comment: This paper has been withdrawn for changes on i

Extreme binary black holes in a physical representation

Stationary axisymmetric binary systems of unequal co and counter-rotating extreme Kerr black holes apart by a conical singularity are studied. Both solutions are well identified as two $3$-parametric subfamilies of the Kinnersley-Chitre metric, and fully depicted by Komar parameters: the two masses $M_{1}$ and $M_{2}$, and a coordinate distance $R$, where the angular momenta $J_{1}$ and $J_{2}$ are functions of these parameters. Our physical representation allows us to identify some limits and novel physical properties.Comment: 11 pages, 6 figures, 1 table; minor change

Corotating dyonic binary black holes

This paper is dedicated to derive and study binary systems of identical corotating dyonic black holes separated by a massless strut -- two 5-parametric corotating binary black hole models endowed with both electric and magnetic charges-- where the dyonic black holes carrying equal/opposite electromagnetic charges in the first/second model satisfy the extended Smarr formula for the mass including the magnetic charge as a fourth conserved parameter.Comment: 12 pages, 1 figure, published versio