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Title: 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:
 [1];  [2]
  1. Department of Physics and Astronomy, Barnard College of Columbia University, 3009 Broadway, New York, New York 10027 (United States)
  2. 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}
}