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arXiv · gr-qc/9710037

Quadrupole-quadrupole gravitational waves

Luc Blanchet
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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.

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Luc Blanchet. 1997-10-07. Quadrupole-quadrupole gravitational waves. https://doi.org/10.1088/0264-9381%2F15%2F1%2F008

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