Static two-body potential at fifth post-Newtonian order

Abstract

We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant GN, in the static limit. This result is achieved within the effective field theory approach to General Relativity, and exploits a manifest factorization property of static diagrams which allows to derive static post Newtonian (PN) contributions of (2n+1)-order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.

7 pages, 3 figures. In v2: references added, published on PRL

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Cited by in corpus (10)

• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Classical gravitational scattering from a gauge-invariant double copy
• Calculating the static gravitational two-body potential to fifth post-Newtonian order with Feynman diagrams