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

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.

arXiv comment20 pages, 9 figures Revised version: added clarifying remarks to introduction and summary; additional table; results and conclusions unchanged. Accepted version for Class. Quant. Grav

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• Internal structures and circular orbits for test particles
• Extreme Mass-Ratio Binary Black Hole Merger: Characteristics of the Test-Particle Limit
• Field theoretical approach to gravitational waves
• Gravitational waves from generalized newtonian sources
• Spin-induced motion in black hole spacetime