Solving the two body problem in Einstein's gravity

The two body problem in Einstein's gravity has both intrinsic theoretical interest, as well as importance for the ongoing observational search for gravitational waves. This talk will explain how field theory ideas and techniques were used 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 approach is known as the Effective Field Theory approach to General Relativity.