Year: 2026
Type: preprint
Abstract: We present a complete analytic expression for the $N$-body Hamiltonian of nonspinning point particles at second post-Newtonian (2PN) order in the Arnowitt-Deser-Misner (ADM) gauge. Recent work reduced the general $N$-body Hamiltonian to a form containing a single unresolved integral term, which prevented a fully explicit closed-form representation. Here, we evaluate this integral analytically and thereby obtain a fully explicit closed-form expression for the general 2PN $N$-body Hamiltonian. We outline the main steps of the derivation and validate the analytic expression through direct numerical comparisons with the original integral representation.
Source: arXiv (Cornell University)
Institution: Friedrich Schiller University Jena
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213432268