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

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.