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Classification of radial Kerr geodesic motion

par Compère, Geoffrey ;Liu, Yan;Long, Jiang
Référence Physical Review D, 105, 2, 024075
Publication Publié, 2022-01-01

Article révisé par les pairs

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Résumé :

We classify radial timelike geodesic motion of the exterior nonextremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first-order radial geodesic equation, using a novel compact notation and by implementing the constraints from polar, time, and azimuthal motion. Four generic root structures with only simple roots give rise to eight nongeneric root structures when either one root becomes coincident with the horizon, one root vanishes, or two roots becomes coincident. We derive the explicit phase space of all such root systems in the basis of energy, angular momentum, and Carter's constant and classify whether each corresponding radial geodesic motion is allowed or disallowed from the existence of polar, time, and azimuthal motion. The classification of radial motion within the ergoregion for both positive and negative energies leads to six distinguished values of the Kerr angular momentum. The classification of null radial motion and near-horizon extremal Kerr radial motion are obtained as limiting cases and compared with the literature. We explicitly parametrize the separatrix describing root systems with double roots as the union of the following three regions that are described by the same quartic respectively obtained when (1) the pericenter of bound motion becomes a double root, (2) the eccentricity of bound motion becomes zero, and (3) the turning point of unbound motion becomes a double root.