Extended multi-soliton solutions of the Einstein field equations: II. Two comments on the existence of equilibrium states

The results of our previous paper are applied to solving analytically the balance problem in the double-Kerr solution for all three possible types of binary systems, i.e. when a binary system is composed of two non-extreme black holes, of a non-extreme black hole and a hyperextreme object and of two hyperextreme objects. We also construct a new stationary electrovacuum metric representing binary systems of charged, magnetized, rotating, aligned masses involving one extreme object and on the basis of the numerical study of balance equations we conjecture that the equilibrium states in such systems are impossible.