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

TL;DR

This paper develops a third post-Newtonian accurate quasi-Keplerian parametrization for eccentric orbits of compact binaries, aiding gravitational wave detection and analysis of relativistic binary pulsars.

Contribution

It provides explicit 3PN orbital elements in both ADM and harmonic coordinates, enhancing waveform modeling and compatibility with numerical simulations.

Findings

Explicit 3PN orbital elements in ADM and harmonic coordinates

Facilitates construction of accurate gravitational wave templates

Aids analysis of relativistic binary pulsar timing

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.