Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits
General Relativity and Quantum Cosmology
2026-01-14 v1 High Energy Astrophysical Phenomena
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
This work is based on the letter Phys. Lett. B, 865, 139484 (2025), where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian order in General Relativity for a compact binary system moving on eccentric orbits. The aim of this paper is to provide more details about the performed calculations and to produce other new results. More specifically, we will focus on deriving the analytical expression of the coordinate time at the second Post-Newtonian order for circular orbits and then discuss two astrophysical applications involving binary neutron star and black hole systems.
Cite
@article{arxiv.2510.20935,
title = {Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits},
author = {Vittorio De Falco and Marco Gallo},
journal= {arXiv preprint arXiv:2510.20935},
year = {2026}
}
Comments
12 pages; 3 figures; 3 tables; 1 appendix