All-order structure of static gravitational interactions and the seventh post-Newtonian potential
Giacomo Brunello, Manoj K. Mandal, Pierpaolo Mastrolia, Raj Patil, Matteo Pegorin + 2 more
TLDR
This paper introduces a closed formula for all-order static post-Newtonian gravitational corrections, confirming 7PN results.
Key contributions
- Developed a closed formula for all-order static post-Newtonian corrections in two-body gravity.
- Derived the formula using a correlation function framework and exploiting $\mathbb{Z}_2$ symmetry.
- Offers a novel theoretical interpretation of the factorization theorem in gravitational dynamics.
- Successfully computed the seventh post-Newtonian order gravitational interaction, matching diagrammatic results.
Why it matters
This work provides a powerful new theoretical tool for calculating gravitational interactions, especially for compact objects. It simplifies complex calculations and validates existing methods, advancing our understanding of general relativity in extreme conditions.
Original 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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