Quadrupole-quadrupole gravitational waves

TL;DR

This paper analyzes the non-linear interactions of quadrupole gravitational waves, deriving new local and non-local effects, and completing the observable quadrupole moment at 5/2 post-Newtonian order.

Contribution

It provides a detailed computation of local and non-local effects in quadrupole-quadrupole gravitational wave interactions, extending the observable quadrupole moment to higher post-Newtonian order.

Findings

Recovery of known non-local modifications of ADM mass-energy.

Calculation of local instantaneous terms associated with non-local effects.

Extension of the observable quadrupole moment to 5/2 post-Newtonian order.

Abstract

This paper investigates the non-linear self-interaction of quadrupole gravitational waves generated by an isolated system. The vacuum Einstein field equations are integrated in the region exterior to the system by means of a post-Minkowskian algorithm. Specializing in the quadrupole-quadrupole interaction (at the quadratic non-linear order), we recover the known results concerning the non-local modification of the ADM mass-energy of the system accounting for the emission of quadrupole waves, and the non-local memory effect due to the re-radiation by the stress-energy distribution of linear waves. Then we compute all the local (instantaneous) terms which are associated in the quadrupole-quadrupole metric with the latter non-local effects. Expanding the metric at large distances from the system, we obtain the corresponding radiation-field observables, including all non-local and transient contributions. This permits notably the completion of the observable quadrupole moment at the 5/2 post-Newtonian order.