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Spherical orbits around a Kerr black hole
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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.
Forward citations
Cited by 2 Pith papers
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Radii of spherical timelike geodesics in Kerr-Newman black holes
Closed-form and numerical radii, existence conditions, and radial stability are given for spherical timelike orbits in Kerr-Newman spacetimes, including an analytical ISCO radius formula.
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Spherical photon orbits around the Kerr-like black hole in Einstein-Bumblebee gravity
In Einstein-Bumblebee Kerr-like spacetimes, spherical photon orbits are governed by a sixth-order polynomial whose roots and critical inclination angle depend on the Lorentz-violation parameter.
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