Isofrequency pairing of geodesic orbits in Kerr geometry

TL;DR

This paper reveals that in Kerr black hole spacetimes, different bound geodesic orbits can share identical fundamental frequencies despite having distinct parameters, indicating a non-unique frequency-to-orbit mapping.

Contribution

It uncovers the existence of isofrequency pairs of geodesic orbits in Kerr geometry, showing the non-uniqueness of frequency characterization of orbits.

Findings

Existence of isofrequency pairs of geodesic orbits

Different orbits can have identical radial, azimuthal, and Lense-Thirring frequencies

Implications for orbit identification in gravitational wave analysis

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.