**Authors**: Rebecca Grossman, Janna Levin, Gabe Perez-Giz

**Date**: 29 May 2011

**Abstract**: Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a classification scheme for these intricate orbits in terms of periodic orbits. The crucial insight is that for a given effective angular momentum $L$ and angle of inclination $\iota$, there exists a discrete set of orbits that are geometrically $n$-leaf clovers in a precessing {\it orbital plane}. When viewed in the full three dimensions, these orbits are periodic in $r-\theta$. Each $n$-leaf clover is associated with a rational number, $1+q_{r\theta}=\omega_\theta/\omega_r$, that measures the degree of perihelion precession in the precessing orbital plane. The rational number $q_{r\theta}$ varies monotonically with the orbital energy and with the orbital eccentricity. Since any bound orbit can be approximated as near one of these periodic $n$-leaf clovers, this special set offers a skeleton that illuminates the structure of all bound Kerr orbits, in or out of the equatorial plane.

1105.5811
(/preprints)

2011-06-01, 11:54
**[edit]**

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

*Tantum in modicis, quantum in maximis*