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Radiative multipole moments of integer-spin fields in curved spacetime
General Relativity and Quantum Cosmology · Submitted 8 May 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type.
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The abstract, sentence by sentence
Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. At second order in v, additional terms appear inside the spatial integrals. These are near-zone corrections which depend on the detailed behavior of the source. At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. | contribution 0.98 | 0.94 | 0.11 | asserted 1.00 |
| s1 | To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. | result 0.97 | 0.67 | 0.07 | asserted 1.00 |
| s2 | At second order in v, additional terms appear inside the spatial integrals. | result 0.99 | 0.83 | 0.04 | asserted 1.00 |
| s3 | These are near-zone corrections which depend on the detailed behavior of the source. | result 0.80 | 0.66 | 0.03 | asserted 1.00 |
| s4 | At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. | result 0.98 | 0.85 | 0.13 | asserted 1.00 |
| s5 | These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. | interpretation 0.99 | 0.39 | 0.13 | hedged possibility 0.71 |
| s6 | Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. | result 1.00 | 0.96 | 0.57 | asserted 1.00 |
| s7 | We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections. | result 1.00 | 0.93 | 0.15 | asserted 1.00 |
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Original abstract
Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. At second order in v, additional terms appear inside the spatial integrals. These are near-zone corrections which depend on the detailed behavior of the source. At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections.
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Then, equation * if $s=-1$ it holds that [equation] * if $s=1$, it holds that [equation] * we have the following relation between $‖φ‖_L^2()$ and $‖' φ‖_L^2()$: [equation] The first claim appears in [ref] .
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