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

TL;DR

This paper advances the analytical understanding of the gravitational self-force for eccentric orbits around a Schwarzschild black hole by extending post-Newtonian calculations up to high orders and validating against numerical data.

Contribution

It provides high-order analytical expansions of the redshift invariant and effective-one-body potentials for eccentric orbits, improving precision in gravitational self-force modeling.

Findings

Analytical expansions up to 9.5PN order for $e^2$ and $e^4$ terms.

Extended analytical knowledge of EOB potentials $ar d(u)$, $ ho(u)$, and $q(u)$.

Results are consistent with existing numerical self-force data.

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.