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.
| Original language | English |
|---|---|
| Article number | 084012 |
| Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |
| Volume | 87 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Apr 3 2013 |
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All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
Cite this
Isofrequency pairing of geodesic orbits in Kerr geometry. / Warburton, Niels; Barack, Leor; Sago, Norichika.
In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 87, No. 8, 084012, 03.04.2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Isofrequency pairing of geodesic orbits in Kerr geometry
AU - Warburton, Niels
AU - Barack, Leor
AU - Sago, Norichika
PY - 2013/4/3
Y1 - 2013/4/3
N2 - 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.
AB - 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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U2 - 10.1103/PhysRevD.87.084012
DO - 10.1103/PhysRevD.87.084012
M3 - Article
VL - 87
JO - Physical review D: Particles and fields
JF - Physical review D: Particles and fields
SN - 1550-7998
IS - 8
M1 - 084012
ER -