  Recent astrophysical models predict that stellar-mass binary black holes
(BBHs) could form and coalesce within a few gravitational radii of a
supermassive black hole (SMBH). Detecting the gravitational waves (GWs) from
such systems requires numerical tools which can track the dynamics of the
binaries while capturing all the essential relativistic effects. This work
develops upon our earlier study of a BBH moving along a circular orbit in the
equatorial plane of a Kerr SMBH. Here we modify the numerical method to
simulate a BBH falling toward the SMBH along a parabolic orbit of arbitrary
inclination with respect to the equator. By tracking the evolution in a frame
freely falling alongside the binary, we find that the eccentricity of the BBH
is more easily excited than it is in the previous equatorial case, and that the
cause is the asymmetry of the tidal tensor imposed on the binary when the
binary moves out of the equatorial plane. Since the eccentricity reaches
maximum around the same time that the BBH becomes the closest to the SMBH,
multi-band GW bursts could be produced which are simultaneously detectable by
the space- and ground-based detectors. We show that the effective spins of such
GW events also undergo significant variation due to the rapid reorientation of
the inner BBHs during their interaction with SMBHs. These results demonstrate
the richness of three-body dynamics in the region of strong gravity, and
highlight the necessity of building new numerical tools to simulate such
systems.
