Solving post-Newtonian accurate Kepler Equation
Yannick Boetzel, Abhimanyu Susobhanan, Achamveedu Gopakumar, Antoine, Klein, Philippe Jetzer
TL;DR
This paper presents an analytical solution to the 3PN-accurate Kepler equation, enabling precise modeling of eccentric binary orbits for gravitational wave detection.
Contribution
It introduces a novel analytical method for solving the 3PN Kepler equation and compares it with numerical solutions for validation.
Findings
Analytical solution matches numerical results closely.
Method facilitates computation of accurate gravitational wave templates.
Enhances modeling of eccentric inspiraling binary systems.
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.
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