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.