Spherical orbits around a Kerr black hole

Abstract

A special class of orbits known to exist around a Kerr black hole are spherical orbits -- orbits with constant coordinate radii that are not necessarily confined to the equatorial plane. Spherical time-like orbits were first studied by Wilkins almost 50 years ago. In the present paper, we perform a systematic and thorough study of these orbits, encompassing and extending previous works on them. We first present simplified forms for the parameters of these orbits. The parameter space of these orbits is then analysed in detail; in particular, we delineate the boundaries between stable and unstable orbits, bound and unbound orbits, and prograde and retrograde orbits. Finally, we provide analytic solutions of the geodesic equations, and illustrate a few representative examples of these orbits.

40 pages, published version

References in corpus (4)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Astrophysically relevant bound trajectories around a Kerr black hole
• A geometric origin for quasi-periodic oscillations in black hole X-ray binaries
• Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time

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