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Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates

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arxiv 2011.10000 v2 pith:KZP5LTNS submitted 2020-11-19 gr-qc hep-th

Luc Blanchet , Geoffrey Compère , Guillaume Faye , Roberto Oliveri , Ali Seraj This is my paper
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keywords metriccoordinatessourcebondiexpansionharmonicmassmultipole
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We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.

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Cited by 3 Pith papers

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