Ballistic orbits in Schwarzschild space-time and gravitational waves from EMR binary mergers

TL;DR

This paper analyzes special ballistic geodesics in Schwarzschild spacetime, deriving analytic source terms for gravitational wave equations and computing waveforms during the plunge phase of EMR black-hole mergers.

Contribution

It introduces a class of ballistic geodesics degenerate with stable circular orbits and provides analytic expressions for gravitational wave source terms during binary infall.

Findings

Derived analytic source terms for Regge-Wheeler and Zerilli-Moncrief equations.

Computed gravitational waveforms during the plunge phase of EMR mergers.

Established a geodesic framework for modeling the plunge in binary coalescence.

Abstract

We describe a special class of ballistic geodesics in Schwarzschild space-time, extending to the horizon in the infinite past and future of observer time, which are characterized by the property that they are in 1-1 correspondence, and completely degenerate in energy and angular momentum, with stable circular orbits. We derive analytic expressions for the source terms in the Regge-Wheeler and Zerilli-Moncrief equations for a point-particle moving on such a ballistic orbit, and compute the gravitational waves emitted during the infall in an Extreme Mass Ratio black-hole binary coalescence. In this way a geodesic description for the plunge phase of compact binaries is obtained.