From Boundary Data to Bound States
The talk is split in two chapters. After a brief introduction to the binary inspiral problem and the motivation to pursue high-accuracy computations, in the first part I will demonstrate how the seemingly unrelated scattering problem carries all the relevant information to compute gravitational observables for elliptic orbits via a “boundary to bound” (B2B) dictionary — without ever resorting to a Hamiltonian. In the second part, I will show how an effective field theory (EFT) approach to the two-body problem in general relativity, together with modern integration methods from particle physics, allow us to systematically (and very efficiently) obtain the scattering data to input in the B2B map. As a paradigmatic example, I readily derive all the adiabatic invariants for bound states of non-spinning compact objects to third order in Newton’s constant and to all orders in the relative velocity — known as the third "Post-Minkowskian" order — from a computation of the scattering angle in the EFT approach.