Effective two-body approach to the hierarchical three-body problem

The motion of three bodies can be solved perturbatively when a tightly bound inner binary is orbited by a distant perturber, giving rise for example to the well-known Kozai-Lidov oscillations. We propose to study the relativistic hierarchical three-body orbits by adapting the Effective Field Theory techniques used in the two-body problem. This allows us to conveniently treat the inner binary as an effective point-particle, thus reducing the complexity of the three-body problem to a simpler spinning two-body motion. We present in details the mapping between the inner binary osculating elements and the resulting spin of the effective point-particle. Our study builds towards a derivation of three-body analytic waveforms.