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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 equilibrium configurations consisting oftwo aligned rotating black holes. Our discussion is principally aimed atdeveloping the ideas of the proof and summarizing the results of two precedingpapers (Neugebauer and Hennig, 2009 [29], Hennig and Neugebauer, 2011 [12]).From a mathematical point of view, this paper is a further example (Meinel etal., 2008 [22]) for the application of the inverse ("scattering") method to anon-linear elliptic differential equation.

Stationary two-black-hole configurations: A non-existence proof