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

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