All-order structure of static gravitational interactions and the seventh post-Newtonian potential
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910132178255872 |
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| author | Brunello, Giacomo Mandal, Manoj K. Mastrolia, Pierpaolo Patil, Raj Pegorin, Matteo Smith, Sid Steinhoff, Jan |
| author_facet | Brunello, Giacomo Mandal, Manoj K. Mastrolia, Pierpaolo Patil, Raj Pegorin, Matteo Smith, Sid Steinhoff, Jan |
| contents | We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All-order structure of static gravitational interactions and the seventh post-Newtonian potential Brunello, Giacomo Mandal, Manoj K. Mastrolia, Pierpaolo Patil, Raj Pegorin, Matteo Smith, Sid Steinhoff, Jan High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem. |
| title | All-order structure of static gravitational interactions and the seventh post-Newtonian potential |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.14134 |