Gravitational scattering, post-Minkowskian approximation, and effective-one-body theory

A novel approach to the effective-one-body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities) and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric, and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective-one-body description of two masses interacting via tensor-scalar gravity.