Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism

TLDR: In this paper, the authors compute the O(m) conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass m moving around a Schwarzschild black hole of mass M?m.

Abstract: Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the O(m) conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass m moving around a Schwarzschild black hole of mass M?m. Specifically, we study the gauge-invariant function ?(x), where ? is defined as the O(m) part of the dimensionless ratio (??r/???)2 between the squares of the radial and azimuthal frequencies of the orbit, and where x=[Gc-3(M+m)???]2/3 is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function ?(x) in the interval 0