Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of a universal inequality between angular momentum and horizon area that has to be satisfied by every sub-extremal black hole, we prove the non-existence of the equilibrium situation in question.