  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. Based on the solution of a boundary problem for disconnected (Killing)
horizons and the resulting violation of characteristic black hole properties,
we present a non-existence proof for the equilibrium configuration in question.
From a mathematical point of view, this result is a further example for the
efficiency of the inverse ("scattering") method in non-linear theories.
