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

2004/07/13 by Raoul-Martin Memmesheimer, A. Gopakumar, Achamveedu Gopakumar +1 · 14 citations
Earth and Planetary Sciences · Physics and Astronomy · #Astrophysical Phenomena and Observations #Geophysics and Gravity Measurements #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.1103/physrevd.70.104011

published as Phys.Rev.D70:104011,2004 · 33 pages, 1 figure

arxiv created 2004/07/13 · openalex publication_date 2004/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two nonspinning 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-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. Because of 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.

Citations

• The double pulsar -- A new testbed for relativistic gravity
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

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• BINARY BLACK HOLE MERGER IN GALACTIC NUCLEI: POST-NEWTONIAN SIMULATIONS
• Deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction
• Dynamical Evolution and Leading Order Gravitational Wave Emission of Riemann-S Binaries
• Strong-Field Gravity Tests with the Double Pulsar
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries