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Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits

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arxiv gr-qc/0407049 v1 pith:45KO6JJF submitted 2004-07-13 gr-qc

Raoul-Martin Memmesheimer , Achamveedu Gopakumar , Gerhard Schäfer This is my paper · ORCID
classification gr-qc
keywords accurateparametrizationpost-newtoniancompactbinarieseccentricorbitalelements
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We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are explicitly given in terms of the 3PN accurate conserved orbital energy and angular momentum in both Arnowitt, Deser, and Misner-type and harmonic coordinates. Our representation will be required to construct post-Newtonian accurate `ready to use' search templates for the detection of gravitational waves from compact binaries in inspiralling eccentric orbits. Due to the presence of certain 3PN accurate gauge invariant orbital elements, the parametrization should be useful to analyze the compatibility of general relativistic numerical simulations involving compact binaries with the corresponding post-Newtonian descriptions. If required, the present parametrization will also be needed to compute post-Newtonian corrections to the currently employed `timing formula' for the radio observations of relativistic binary pulsars.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order

    gr-qc 2025-11 unverdicted novelty 8.0 of 10

    Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.

  2. High-Post-Newtonian-Order Dynamics Induced by Tail-of-Tail Interactions: The Non-Geodesic Terms

    gr-qc 2026-08 conditional novelty 7.0 of 10

    The authors compute tail-of-tail contributions to the effective-one-body Q potential through p_r^12 and derive new second-order self-force redshift predictions for eccentric binaries.

  3. Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model SEOBNRv6EHM

    gr-qc 2026-05 unverdicted novelty 7.0 of 10

    SEOBNRv6EHM is a multipolar EOB model for eccentric planar-orbit BBHs calibrated to NR simulations, showing low waveform mismatches up to eccentricity 0.9.

  4. Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order

    gr-qc 2024-12 conditional novelty 7.0 of 10

    Tidal contributions to all gravitational waveform amplitude modes up to l=7 are derived to 2.5PN for quasi-circular non-spinning compact binaries, with flux and phasing provided at the same order.

  5. Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM

    gr-qc 2024-12 conditional novelty 7.0 of 10

    The authors obtain, for the first time, 3PN-accurate eccentric-orbit fluxes, radiation-reaction force, and waveform modes in the effective-one-body formalism, and use them to build the SEOBNRv5EHM inspiral model.

  6. Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM

    gr-qc 2024-12 conditional novelty 7.0 of 10

    SEOBNRv5EHM, a new effective-one-body waveform model with third-post-Newtonian eccentricity corrections, reaches a median 0.02% mismatch against eccentric numerical-relativity simulations, about an order of magnitude ...

  7. Analytical Solution of Spinning, Eccentric Binary Black Hole Dynamics at the Second Post-Newtonian Order

    gr-qc 2026-03 unverdicted novelty 6.0 of 10

    An analytical 2PN solution is constructed for the orbital and spin dynamics of eccentric, arbitrarily spinning binary black holes, with spin oscillations retained only at 1.5PN accuracy.

  8. Dynamics of Relativistic Binaries in Structured and Stochastic Environments: A Lagrange-Fourier-Hansen Framework

    gr-qc 2026-06 unverdicted novelty 5.0 of 10

    A new framework projects perturbations onto resonant frequencies via Hansen coefficients to produce efficient coupled ODEs for orbital elements in GW-driven relativistic binaries, demonstrated on tidal fields and accr...

  9. Eccentricity Effects on Modeling Dynamic Quantities and Their Correlations in Binary Black Hole Mergers

    gr-qc 2025-01 conditional novelty 5.0 of 10

    Varying the initial orbital phase of an eccentric binary black hole at fixed eccentricity produces an envelope of radiated energy, momentum, and spin, so eccentric mergers span broad domains of remnant properties rela...

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