We investigate the role of the Keplerian tidal field generated by a supermassive black hole (SMBH) on the three-body dynamics of stellar mass black holes. We consider two scenarios occurring close to the SMBH: the breakup of unstable triples and three-body encounters between a binary and a single. These two cases correspond to the hard and soft binary cases, respectively. The tidal field affects the breakup of triples by tidally limiting the system, so that the triples break earlier with lower breakup velocity, leaving behind slightly larger binaries (relative to the isolated case). The breakup direction becomes anisotropic and tends to follow the shape of the Hill region of the triple, favoring breakups in the radial direction. Furthermore, the tidal field can torque the system, leading to angular momentum exchanges between the triple and its orbit around the SMBH. This process changes the properties of the final binary, depending on the initial angular momentum of the triple. Finally, the tidal field also affects binary-single encounters: binaries tend to become both harder and more eccentric with respect to encounters that occur in isolation. Consequently, single-binary scattering in a deep Keplerian potential produces binaries with shorter gravitational wave merger timescales.
