Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

摘要: We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and linear order in mass ratio, radial potential describing (within effective one-body formalism) gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical self-force theory (for a particle circular orbit around Schwarzschild black hole) Detweiler's gauge-invariant redshift variable. emphasize increase \lq\lq transcendentality" numbers entering expansion coefficients as increases, particular we note appearance $\zeta(3)$ (as well square Euler's constant $\gamma$) starting at seventh order. study convergence parameter $u=GM/(c^2r)$ leaves weak-field domain $u\ll 1$ enter strong field $u=O(1)$.