Spherical orbits around a Kerr black hole

2020/07/08 by Edward Teo · 1 voice · 6 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #gr-qc

paper · pdf · doi:10.1007/s10714-020-02782-z

openalex created_date 2020/07/16 · openalex publication_date 2021/01/01 · openalex updated_date 2026/07/29

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.

Citations

• Spherical Photon Orbits Around a Kerr Black Hole
• Global Structure of the Kerr Family of Gravitational Fields
• Observation of Gravitational Waves from a Binary Black Hole Merger
• Location of the last stable orbit in Kerr spacetime

Cited by

• Calculating black hole shadows: Review of analytical studies
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane
• Black Holes with Accretion Disks as High-Energy Particle Colliders
• Parameter Estimation of Magnetised Kerr Black Holes Using Their Shadows
• Precession of spherical orbits for the spacetime without ℤ₂ symmetry induced by NUT charge
• From quasi-local definitions to a dynamical potential: A unified framework for evolving circular orbits in dynamical spacetimes

Discussions

• A spherical orbit is an orbit around a Kerr black hole which remains at a constant radial coordinate $r$ , but does not remain at a constant polar angle $\theta$ . Orbits such as this arise when the C [stackexchange, 6 points]

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• The Analytical Solutions of Equatorial Geodesic Motion in Kerr Spacetime
• Spherical photon orbits around Kerr-MOG black hole
• Orbits around a Kerr black hole and its shadow