  Nuclear star clusters around massive black holes are expected to be abundant
in stellar mass black holes and black hole binaries. These binaries form a
hierarchical triple system with the massive black hole at the center.
Gravitational perturbations from the massive black hole can cause high
eccentricity excitation. During this process, the eccentricity may approach
unity, and the pericenter distance may become sufficiently small that
gravitational wave emission drives the binary to merge. In this paper, we
consider a simple proof of concept and explore the effect of the eccentric
Kozai-Lidov mechanism for unequal mass binaries. We perform a set of Monte
Carlo simulations on BH-BH binaries in galactic nuclei with quadrupole and
octupole-level secular perturbations, general relativistic precession, and
gravitational wave emission. For a nominal number of steady-state BH-BH
binaries, our model gives a total merger rate $\sim 1 - 3$$Gpc^{-3} yr^{-1}$,
depending on the assumed density profile. Thus, our model potentially competes
with other dynamical mechanisms, such as the dynamical formations and mergers
of BH binaries in globular clusters or dense nuclear clusters without a massive
black hole. We provide predictions for the distributions of these LIGO sources
in galactic nuclei.
