From boundary data to bound states. Part III. Radiative effects

Abstract

We extend the boundary-to-bound (B2B) correspondence to incorporate radiative as well as conservative radiation-reaction effects. We start by deriving a map between the total change in observables due to gravitational wave emission during hyperbolic-like motion and in one period of an elliptic-like orbit, which is valid in the adiabatic expansion for non-spinning as well as aligned-spin configurations. We also discuss the inverse problem of extracting the associated fluxes from scattering data. Afterwards we demonstrate, to all orders in the Post-Minkowskian expansion, the link between the radiated energy and the ultraviolet pole in the radial action in dimensional regularization due to tail effects. This implies, as expected, that the B2B correspondence for the conservative sector remains unchanged for local-in-time radiation-reaction tail effects with generic orbits. As a side product, this allows us to read off the energy flux from the associated pole in the tail Hamiltonian. We show that the B2B map also holds for non-local-in-time terms, but only in the large-eccentricity limit. Remarkably, we find that all of the trademark logarithmic contributions to the radial action map unscathed between generic unbound and bound motion. However, unlike logarithms, other terms due to non-local effects do not transition smoothly to quasi-circular orbits. We conclude with a discussion on these non-local pieces. Several checks of the B2B dictionary are displayed using state-of-the-art knowledge in Post-Newtonian/Minkowskian theory.