Solving post-Newtonian accurate Kepler Equation

Abstract

We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional analytic solution is presented to check the correctness of our compact solution and we perform comparisons between our PN-accurate analytic solution and a very accurate numerical solution of the PN-accurate Kepler equation. We adapt our approach to compute crucial 3PN-accurate inputs that will be required to compute analytically both the time and frequency domain ready-to-use amplitude-corrected PN-accurate search templates for compact binaries in inspiralling eccentric orbits.

20 pages, 4 figures

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Cited by in corpus (42)

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• Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism
• A 3PN Fourier Domain Waveform for Non-Spinning Binaries with Moderate Eccentricity
• A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity
• Gravitational Waves Probes of Parity Violation in Compact Binary Coalescence
• Fourier domain gravitational waveforms for precessing eccentric binaries
• Solving post-Newtonian accurate Kepler Equation
• Accuracy of Estimating Highly Eccentric Binary Black Hole Parameters with Gravitational-Wave Detections
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• Improved post-Newtonian waveform model for inspiralling precessing-eccentric compact binaries
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• High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model
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• Combining Post-Circular and Padé approximations to compute Fourier domain templates for eccentric inspirals
• Efficient gravitational-wave model for fully-precessing and moderately-eccentric, compact binary inspirals
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• Eccentric Catastrophes & What To Do With Them
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• Analytical coordinate time at the second post-Newtonian order
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework