Isofrequency pairing of geodesic orbits in Kerr geometry

Niels Warburton, Leor Barack, and Norichika Sago
Phys. Rev. D 87, 084012 – Published 3 April 2013

Abstract

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum, and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal, and (mean) azimuthal motions. Here, we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair, the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain “synchronized” in phase.

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  • Received 16 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.084012

© 2013 American Physical Society

Authors & Affiliations

Niels Warburton1,2, Leor Barack2, and Norichika Sago3

  • 1School of Mathematical Sciences and Complex and Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland
  • 2School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • 3Faculty of Arts and Science, Kyushu University, Fukuoka 819-0395, Japan

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Vol. 87, Iss. 8 — 15 April 2013

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