A periodic table for black hole orbits
Abstract
Understanding the dynamics around rotating black holes is imperative to the success of future gravitational wave observatories. Although integrable in principle, testparticle 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 strongfield 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 strongfield regime past which zoomwhirl 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.
 Publication:

Physical Review D
 Pub Date:
 May 2008
 DOI:
 10.1103/PhysRevD.77.103005
 arXiv:
 arXiv:0802.0459
 Bibcode:
 2008PhRvD..77j3005L
 Keywords:

 97.60.Lf;
 04.70.s;
 95.30.Sf;
 Black holes;
 Physics of black holes;
 Relativity and gravitation;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 42 pages, lots of figures