Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions
Abstract
For eccentric systems with aligned spins, we compute all spin contributions to the gauge-invariant conservative map between the constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) frequencies at the fourth post-Newtonian order. This extends the nonspinning map derived in [arXiv:2511.10735] to include terms that are linear, quadratic, cubic, and quartic in spin, as well as the associated spin-deformability parameters. We also obtain derived quantities such as the redshift and gyroscopic invariants, as well as circular links. We notice that the Blanchet-Iyer-Favata post-Newtonian stability criterion that determines the dimensionless frequency of the innermost stable circular orbit (ISCO) is in fact intricately related to the periastron advance for circular orbits. Finally, in the case of unbound orbits, we complete the 4PN scattering angle with all spin contributions.
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BibTeX
@misc{trestini2026constants,
title = {{Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions}},
author = {David Trestini and Jan Steinhoff},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.31072},
eprint = {2608.31072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31072},
}
RIS
TY - UNPB
TI - Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions
AU - David Trestini
AU - Jan Steinhoff
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.31072
UR - https://arxiv.org/abs/2608.31072
AB - For eccentric systems with aligned spins, we compute all spin contributions to the gauge-invariant conservative map between the constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) frequencies at the fourth post-Newtonian order. This extends the nonspinning map derived in [arXiv:2511.10735] to include terms that are linear, quadratic, cubic, and quartic in spin, as well as the associated spin-deformability parameters. We also obtain derived quantities such as the redshift and gyroscopic invariants, as well as circular links. We notice that the Blanchet-Iyer-Favata post-Newtonian stability criterion that determines the dimensionless frequency of the innermost stable circular orbit (ISCO) is in fact intricately related to the periastron advance for circular orbits. Finally, in the case of unbound orbits, we complete the 4PN scattering angle with all spin contributions.
ER -