Gravitational waves from compact binaries in post-Newtonian accurate hyperbolic orbits

TL;DR

This paper develops a third post-Newtonian accurate parametric solution for hyperbolic orbits of non-spinning compact binaries, enabling precise modeling of gravitational waves in such scenarios.

Contribution

It introduces the first third post-Newtonian accurate Keplerian-type parametric solution for hyperbolic orbits, extending previous eccentric orbit models.

Findings

Derived 3PN-accurate hyperbolic orbital elements

Provided a method to model gravitational wave polarization states

Validated the solution through consistency checks

Abstract

We derive from first principles third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN-accurate dynamics of non-spinning compact binaries in hyperbolic orbits. Orbital elements and functions of the parametric solution are obtained in terms of the conserved orbital energy and angular momentum in both Arnowitt-Deser-Misner type and modified harmonic coordinates. Elegant checks are provided that include a modified analytic continuation prescription to obtain our independent hyperbolic parametric solution from its eccentric version. A prescription to model gravitational wave polarization states for hyperbolic compact binaries experiencing 3.5PN-accurate orbital motion is presented that employs our 3PN-accurate parametric solution.