Isofrequency pairing of geodesic orbits in Kerr geometry

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


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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 16 January 2013


© 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

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Vol. 87, Iss. 8 — 15 April 2013

Reuse & Permissions
Access Options
General Relativity Still Making Waves
September 24, 2015

Clifford Will discusses the importance of Einstein’s general theory of relativity and its relevance for physics research today.

General Relativity
2015 - General Relativity’s Centennial

The editors of the Physical Review journals have curated a collection of landmark papers on General Relativity to celebrate its centennial. These papers are currently free to read.

Authorization Required




Sign up to receive regular email alerts from Physical Review D

Log In



Article Lookup

Paste a citation or DOI

Enter a citation