  Increased eccentricity of a black hole binary leads to reduced merger times.
With n-body simulations and analytic approximations including the effects of
general relativity (GR), we show that even a low mass companion orbiting a
black hole binary can cause significant eccentricity oscillations of the binary
as a result of the Kozai-Lidov mechanism. A companion with a mass as low as
about 1% of the binary mass can drive the binary eccentricity up to >~ 0.8,
while a mass of a few percent can drive eccentricities greater than 0.98. For
low mass companions, this mechanism requires the companion to be on an orbit
that is closer to retrograde than to prograde to the binary orbit and this may
occur through capture of the third body. The effects of GR limit the radial
range for the companion for which this mechanism works for the closest
binaries. The merger timescale may be reduced by several orders of magnitude
for a captured companion mass of only a few percent of the binary mass.
