Equilibrium configuration of black holes and inverse scattering method

The inverse scattering method is applied for investigation of equilibrium configuration of black holes. Basing on the study of the boundary problem corresponding to this configuration it is shown that any axially symmetric stationary solution of Einstein equations with disconnected event horison must be contained in the class of Belinskiy–Zaharov solutions. The relations between angular momenta and angular velocities of the black holes are derived.