  Most galaxies have central massive black holes (BH), and merge with others
during their evolution, as strongly suggested by recent observations.
Consequently a black hole binary (BHB) emerges. Considering the evolution of
the binary when it has become hard, at a separation of the BHs of about 1 pc,
we propose to solve two basic questions in our understanding of the central
activity of galaxies: (1) Do the BHs actually merge? (2) And does the effect of
the torque of the BHB on the surrounding stellar distribution help to explain
the presence of the ubiquitous torus of molecular material surrounding
apparently all active galactic nuclei? While the second question is the topic
of a subsequent paper we try to solve the first in this article. Simulating the
evolution of a stellar cluster in the potential of such a binary by solving the
equations of the restricted three body problem, we obtained the following
results: If the cluster is about as massive as the BHB, the two BHs coalesce
after about 10^7 yr due to ejection of stars with low angular momentum and
finally via emission of gravitational radiation. In a sequence of models where
the mass of the secondary BH increases while M_1 is fixed, a bigger fraction of
stars is ejected. For a more massive cluster the merger then proceeds on
smaller time scales. The cluster is depleted in the central region and the
final distribution of stars assumes a torus-like structure, peaking at three
times the initial distance of the two black holes.
