New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole

Abstract

We raise the analytical knowledge of the eccentricity-expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the $e^2$ and $e^4$ contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through $e^{20}$. We convert this information into an analytical knowledge of the effective-one-body radial potentials $\bar{d}(u)$, $\rho (u)$ and $q(u)$ through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.

21 pages; 2 figures (4 eps files); revtex macros used. Revised version including more details in Appendix B. References updated and minor typos corrected

References in corpus (12)

• Fourth post-Newtonian effective one-body dynamics
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Tidal invariants for compact binaries on quasi-circular orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Numerical computation of the EOB potential q using self-force results

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