  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 of
two aligned rotating black holes. Our discussion is principally aimed at
developing the ideas of the proof and summarizing the results of two preceding
papers (Neugebauer and Hennig, 2009 [29], Hennig and Neugebauer, 2011 [12]).
From a mathematical point of view, this paper is a further example (Meinel et
al., 2008 [22]) for the application of the inverse ("scattering") method to a
non-linear elliptic differential equation.
