  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.
