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We extend the analytical determination of the main radial potentialdescribing (within the effective one-body formalism) the gravitationalinteraction of two bodies beyond the 4th post-Newtonian approximation recentlyobtained by us. This extension is done to linear order in the mass ratio byapplying analytical gravitational self-force theory (for a particle in circularorbit around a Schwarzschild black hole) to Detweiler's gauge-invariantredshift variable. By using the version of black hole perturbation theorydeveloped by Mano, Suzuki and Takasugi, we have pushed the analyticaldetermination of the (linear in mass ratio) radial potential to the 6thpost-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). Inprinciple, our analytical method can be extended to arbitrarily highpost-Newtonian orders.

High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations