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

Abstract

We derive from first principles a third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN accurate dynamics of nonspinning 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.