  Mergers of black-hole binaries are expected to release large amounts of
energy in the form of gravitational radiation. However, binary evolution models
predict merger rates too low to be of observational interest. In this paper we
explore the possibility that black holes become members of close binaries via
dynamical interactions with other stars in dense stellar systems. In star
clusters, black holes become the most massive objects within a few tens of
millions of years; dynamical relaxation then causes them to sink to the cluster
core, where they form binaries. These black-hole binaries become more tightly
bound by superelastic encounters with other cluster members, and are ultimately
ejected from the cluster. The majority of escaping black-hole binaries have
orbital periods short enough and eccentricities high enough that the emission
of gravitational waves causes them to coalesce within a few billion years. We
predict a black-hole merger rate of 10^-8 to 10^-7 per year per cubic
megaparsec, implying gravity-wave detection rates substantially greater than
the corresponding rates from neutron star mergers. For the first generation
Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about
one detection during the first two years of operation. For its successor
LIGO-II, the rate rises to roughly one detection per day. There is about an
order of magnitude uncertainty in these numbers.
