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.