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arXiv · 2604.14134

All-order structure of static gravitational interactions and the seventh post-Newtonian potential

Giacomo Brunello·Manoj K. Mandal·Pierpaolo Mastrolia·Raj Patil·Matteo Pegorin·Sid Smith·Jan Steinhoff
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Abstract

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.

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Giacomo Brunello, Manoj K. Mandal, Pierpaolo Mastrolia, Raj Patil, Matteo Pegorin, Sid Smith, Jan Steinhoff. 2026-04-15. All-order structure of static gravitational interactions and the seventh post-Newtonian potential. https://arxiv.org/abs/2604.14134

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