High-order comparisons between post-Newtonian and perturbative self forces

TL;DR

This paper compares high-order post-Newtonian calculations with self-force results for small mass-ratio black-hole binaries, confirming the presence of non-linear tail effects up to 7.5PN order.

Contribution

It extends the PN formalism to include contributions beyond 5.5PN, matching self-force results and clarifying the origin of half-integral PN terms.

Findings

Agreement between PN and SF redshift factors up to 7.5PN.

Identification of tail-of-tail effects as source of half-integral PN terms.

Extension of PN calculations to higher orders.

Abstract

Recent numerical and analytic computations based on the self-force (SF) formalism in general relativity showed that half-integral post-Newtonian (PN) terms, i.e. terms involving odd powers of 1/c, arise in the redshift factor of small mass-ratio black-hole binaries on exact circular orbits. Although those contributions might seem puzzling at first sight for conservative systems that are invariant under time-reversal, they are in fact associated with the so-called non-linear tail-of-tail effect. We shall describe here how the next-to-next-to-leading order contributions beyond the first half-integral 5.5PN conservative effect (i.e. up to order 7.5PN included) have been obtained by means of the standard PN formalism applied to binary systems of point-like objects. The resulting redshift factor in the small mass-ratio limit fully agrees with that of the SF approach.