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 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 results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.