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Using the main result of a companion paper, in which the binding energy of acircular-orbit non-spinning compact binary system is computed at leading-orderbeyond the test-particle approximation, the exact expression of theeffective-one-body (EOB) metric component g^eff_tt is obtained through firstorder in the mass ratio. Combining these results with the recent gravitationalself-force calculation of the periastron advance for circular orbits in theSchwarzschild geometry, the EOB metric component g^eff_rr is also determined atlinear order in the mass ratio. These results assume that the mapping betweenthe real and effective Hamiltonians at the second and third post-Newtonian (PN)orders holds at all PN orders. Our findings also confirm the advantage ofresumming the PN dynamics around the test-particle limit if the goal is toobtain a flexible model that can smoothly connect the test-mass and equal-masslimits.

The complete non-spinning effective-one-body metric at linear order in the mass ratio