Complete the general N-body Hamiltonian at 3PN order

Complete the conservative 3PN description for general N-body systems by deriving the remaining interactions beyond the currently available partial results.

Background

The paper presents a fully explicit conservative Hamiltonian for arbitrary nonspinning point-particle systems at 2PN order in the ADM gauge. It notes that the corresponding general N-body formulation at the next post-Newtonian order remains incomplete. Although some partial 3PN results beyond the two-body problem have been obtained, including specific three-body interaction terms, a complete treatment requires deriving the remaining conservative interactions at 3PN order.

References

However, a fully explicit analytic description of general $N$-body dynamics at 2PN order has remained incomplete until the present work, while the corresponding 3PN description is still incomplete for general $N$-body systems.

— A Fully Analytic Expression for the 2PN N-Body Hamiltonian  (2609.17510 - Heinze et al., 15 Sep 2026) in Section 1, Introduction