**Authors**: Janna Levin, Hugo Contreras

**Date**: 13 Sep 2010

**Abstract**: We compile the equations of motion describing the most general black hole binaries as computed by Will and collaborators. We use the equations converted to Hamiltonian variables to consider spinning and precessing and eccentric pairs. We find that while spin-spin coupling corrections can destroy constant radius orbits in principle, the effect is so small that orbits will reliably tend to quasi-spherical as angular momentum and energy are lost to gravitational radiation. Still, highly eccentric pairs can retain eccentricity by the time of plunge. We also show that three natural frequencies of an orbit demonstrating both spin precession and perihelion precession are the frequency of angular motion in the orbital plane, the frequency of the plane precession, and the frequency of radial oscillations. These three shape the waveform. The pattern of energy lost during the inspiral is also directly related to these same natural harmonics.

1009.2533
(/preprints)

2010-09-15, 05:49
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*