• DOI:10.1103/PhysRevD.77.103005
• Corpus ID: 119204090

A periodic table for black hole orbits

@article{Levin2008APT,
  title={A periodic table for black hole orbits},
  author={Janna Levin and Gabe Perez-Giz},
  journal={Physical Review D},
  year={2008},
  volume={77},
  pages={103005}
}

• J. Levin, Gabe Perez-Giz
• Published 4 February 2008
• Physics
• Physical Review D

Understanding the dynamics around rotating black holes is imperative to the success of future gravitational wave observatories. Although integrable in principle, test-particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multileaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.