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Survey of spinning test particle orbits in Kerr spacetime

Hartl, Michael D. (2003) Survey of spinning test particle orbits in Kerr spacetime. Physical Review D, 67 (10). Art. No. 104023. ISSN 2470-0010.

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We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.

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Additional Information:©2003 The American Physical Society. Received 17 February 2003; published 28 May 2003. I would like to thank Scott Hughes and Teviet Creighton for providing notes on parametrizing Kerr geodesics in terms of orbital parameters. I also thank Sterl Phinney for his careful reading of the manuscript and perceptive comments. This work was supported in part by NASA grant NAG5-10707.
Subject Keywords:chaos; space-time configurations; black holes; Lyapunov methods; gravitation
Issue or Number:10
Record Number:CaltechAUTHORS:HARprd03a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5254
Deposited By: Tony Diaz
Deposited On:06 Oct 2006
Last Modified:02 Oct 2019 23:20

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