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

Abstract

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

13 pages; 1 eps figure. Revtex latex macros used

References in corpus (3)

• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

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