2021
DOI: 10.1007/jhep02(2021)029
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Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

Abstract: 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… Show more

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Cited by 46 publications
(47 citation statements)
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“…(4.16'). 11 The associated D-dimensional terms up to the constant parts were calculated in [16,28], see also [37,47], and do also agree. This concerns the 1PN correction to the electric quadrupole moment, EQ ij Q ji , [37], the octupole moment, EO ijk O ijk , and the magnetic quadrupole moment, EJ ij J ji .…”
Section: The Local Tail Terms Of the Pole-free Hamiltoniansupporting
confidence: 53%
“…(4.16'). 11 The associated D-dimensional terms up to the constant parts were calculated in [16,28], see also [37,47], and do also agree. This concerns the 1PN correction to the electric quadrupole moment, EQ ij Q ji , [37], the octupole moment, EO ijk O ijk , and the magnetic quadrupole moment, EJ ij J ji .…”
Section: The Local Tail Terms Of the Pole-free Hamiltoniansupporting
confidence: 53%
“…However, it does not go as far as introducing a linear divergence in g uu and thus a time dependence of the leading order metric. One reason for this is that g uu = O(1) appears to be sufficient to describe the physics of compact binaries [91,92]. 5 The consequences of these different boundary conditions on the asymptotic symmetry group are discussed in section 4.…”
Section: Jhep07(2021)170mentioning
confidence: 99%
“…The Einstein's equations can be perturbatively solved in harmonic gauge under the assumption of no incoming radiation[91]. Transforming to Bondi or Newman-Unti coordinates one obtains guu = O(1)[92].…”
mentioning
confidence: 99%
“…A widely used gauge to study asymptotic boundaries is the Bondi gauge [1,2,32,33]. Indeed, it is particularly well-adapted to investigate the interplay between radiation and symmetries [17,19,28,[34][35][36][37][38][39]. Furthermore, it allows us to consider simultaneously asymptotically locally flat spacetimes exhibiting null boundaries and asymptotically locally AdS spacetimes with timelike boundaries [26,[40][41][42][43][44][45].…”
Section: Introductionmentioning
confidence: 99%