Abstract : The motion of three bodies can be solved perturbatively when a tightly bound inner binary is orbited by a distant perturber on an elliptic orbit. The exchange of angular momentum between the two orbits gives rise to Kozai-Lidov oscillations of eccentricity and inclination characterizing many different systems in astronomy. In this talk, I will first review the Newtonian version of the Kozai-Lidov mechanism before introducing the effect of relativistic corrections with applications to gravitational wave astronomy. I will show how one can systematically compute first post-Newtonian terms in the hierarchical three-body problem and discuss their influence on the dynamics of the system.
Finally, I will present a new kind of relativistic resonance and its effect on the eccentricity of the inner binary, which could potentially be measurable in the phase of gravitational waves.