Relativistic Dynamics in Black Hole Triples

Binary black holes can be driven to merger by interactions with a third companion via the Lidov-Kozai mechanism. The impact of this mechanism may be observable by LIGO/Virgo through the production of binaries with distinct eccentricity. We present a direct method to derive the orbit averaged gravitational dynamics of a hierarchical three-body system to first post-Newtonian order. We start with the Einstein-Infeld-Hoffman (EIH) equations for a three-body system and write the accelerations as a power series in the ratio of the semi-major axes of the two orbits, (a₁/a₂). At zeroth order, the two orbits evolve independently. At first order, orbital interaction terms (of both Newtonian and relativistic nature) start to appear, and sub-leading interaction terms appear at higher powers in (v/c) and (a₁/a₂). These interaction terms become important when the three-body Newtonian timescales are comparable to the relativistic timescales and provide an analytic description of behavior observed in previous N-body simulations.