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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.02868 |
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| _version_ | 1866913363336888320 |
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| author | Amalberti, Loris Larrouturou, François Yang, Zixin |
| author_facet | Amalberti, Loris Larrouturou, François Yang, Zixin |
| contents | In this paper we study the multipole expansion of the long-wavelength effective action for radiative sources in ($d$+1) spacetime dimensions. We present detailed expressions for the multipole moments for the case of scalar-, electromagnetic-, and (linearized) gravitational-wave emission. For electromagnetism and gravity, we derive expressions for the odd-parity, magnetic-type moments as SO($d$) duals of the ones traditionally used in the literature. The $d$-dimensional case features a novel set of `Weyl-type' moments, coupling to the spatial part of the Weyl tensor, which are absent in three dimensions. Agreement is found in the overlap with previous known results, notably in the $d \to 3$ limit. Due to its reliance on dimensional regularization, the results presented here play a crucial role for the further development of the Effective Field Theory approach to gravitational dynamics, and in particular for the computation of the gravitational-wave flux, starting at the third post-Newtonian order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multipole expansion at the level of the action in $d$-dimensions Amalberti, Loris Larrouturou, François Yang, Zixin General Relativity and Quantum Cosmology In this paper we study the multipole expansion of the long-wavelength effective action for radiative sources in ($d$+1) spacetime dimensions. We present detailed expressions for the multipole moments for the case of scalar-, electromagnetic-, and (linearized) gravitational-wave emission. For electromagnetism and gravity, we derive expressions for the odd-parity, magnetic-type moments as SO($d$) duals of the ones traditionally used in the literature. The $d$-dimensional case features a novel set of `Weyl-type' moments, coupling to the spatial part of the Weyl tensor, which are absent in three dimensions. Agreement is found in the overlap with previous known results, notably in the $d \to 3$ limit. Due to its reliance on dimensional regularization, the results presented here play a crucial role for the further development of the Effective Field Theory approach to gravitational dynamics, and in particular for the computation of the gravitational-wave flux, starting at the third post-Newtonian order. |
| title | Multipole expansion at the level of the action in $d$-dimensions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2312.02868 |