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.