Gravitational-wave tail effects to quartic non-linear order

TL;DR

This paper derives higher-order gravitational-wave tail effects, specifically quartic non-linear interactions at 4.5PN order, and computes their contribution to the energy flux in compact binary systems, confirming consistency with black-hole perturbation results.

Contribution

It introduces the derivation of quartic non-linear tail effects (

Findings

Derived the 4.5PN order tail-of-tails-of-tails effects.

Calculated the complete coefficient for gravitational-wave energy flux at this order.

Confirmed agreement with black-hole perturbation theory in extreme mass ratio limit.

Abstract

Gravitational-wave tails are due to the backscattering of linear waves onto the space-time curvature generated by the total mass of the matter source. The dominant tails correspond to quadratic non-linear interactions and arise at the one-and-a-half post-Newtonian (1.5PN) order in the gravitational waveform. The "tails-of-tails", which are cubic non-linear effects appearing at the 3PN order in the waveform, are also known. We derive here higher non-linear tail effects, namely those associated with quartic non-linear interactions or "tails-of-tails-of-tails", which are shown to arise at the 4.5PN order. As an application, we obtain at that order the complete coefficient in the total gravitational-wave energy flux of compact binary systems moving on circular orbits. Our result perfectly agrees with black-hole perturbation calculations in the limit of extreme mass ratio of the two compact objects.