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

Abstract

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.

33 pages, 1 figure

References in corpus (24)

• The Dynamics of General Relativity
• Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order
• Testing General Relativity with Pulsar Timing
• Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
• Improved filters for gravitational waves from inspiralling compact binaries
• Dimensional regularization of the gravitational interaction of point masses
• Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
• Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Numerical Relativity and Compact Binaries
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?

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