  We map the general relativistic two-body problem onto that of a test particle
moving in an effective external metric. This effective-one-body approach
defines, in a non-perturbative manner, the late dynamical evolution of a
coalescing binary system of compact objects. The transition from the adiabatic
inspiral, driven by gravitational radiation damping, to an unstable plunge,
induced by strong spacetime curvature, is predicted to occur for orbits more
tightly bound than the innermost stable circular orbit in a Schwarzschild
metric of mass M = m1 + m2. The binding energy, angular momentum and orbital
frequency of the innermost stable circular orbit for the time-symmetric
two-body problem are determined as a function of the mass ratio.
