The effective field theory approach uses field theory ideas and techniques to perturbatively solve the two-body problem in the slow velocity post-Newtonian limit.
Central notions include the two-body effective action, field elimination through Feynman diagrams, a non-relativistic decomposition of Einstein's field, and finally divergences, their regularization and renormalization.
This study is important for the ongoing observational effort to detect gravitational waves and it complements numerical simulations.