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, 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.
- Authors:
-
- Department of Physics and Astronomy, Barnard College of Columbia University, 3009 Broadway, New York, New York 10027 (United States)
- Physics Department, Columbia University, New York, New York 10027 (United States)
- Publication Date:
- OSTI Identifier:
- 21210177
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. D, Particles Fields
- Additional Journal Information:
- Journal Volume: 77; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.77.103005; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASTROPHYSICS; BLACK HOLES; GRAVITATIONAL WAVES; KERR EFFECT; ORBITS; PERIODICITY; POTENTIALS; SPACE-TIME; TEST PARTICLES
Citation Formats
Levin, Janna, Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027, and Perez-Giz, Gabe. A periodic table for black hole orbits. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.77.103005.
Levin, Janna, Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027, & Perez-Giz, Gabe. A periodic table for black hole orbits. United States. https://doi.org/10.1103/PHYSREVD.77.103005
Levin, Janna, Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027, and Perez-Giz, Gabe. 2008.
"A periodic table for black hole orbits". United States. https://doi.org/10.1103/PHYSREVD.77.103005.
@article{osti_21210177,
title = {A periodic table for black hole orbits},
author = {Levin, Janna and Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027 and Perez-Giz, Gabe},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.77.103005},
url = {https://www.osti.gov/biblio/21210177},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 77,
place = {United States},
year = {Thu May 15 00:00:00 EDT 2008},
month = {Thu May 15 00:00:00 EDT 2008}
}