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A Fully Analytic Expression for the 2PN N-Body Hamiltonian
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.
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BibTeX
@misc{heinze2026fully,
title = {{A Fully Analytic Expression for the 2PN N-Body Hamiltonian}},
author = {Felix M. Heinze and Gerhard Schäfer and Bernd Brügmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17510},
eprint = {2609.17510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17510},
}
RIS
TY - UNPB
TI - A Fully Analytic Expression for the 2PN N-Body Hamiltonian
AU - Felix M. Heinze
AU - Gerhard Schäfer
AU - Bernd Brügmann
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17510
UR - https://arxiv.org/abs/2609.17510
AB - 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.
ER -