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arXiv · 2207.05594

Bound orbit domains in the phase space of the Kerr geometry

Prerna Rana·A. Mangalam
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Abstract

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter's constant space ($E$, $L$, $a$, $Q$), and eccentricity, inverse-latus rectum space ($e$, $\mu$, $a$, $Q$). These conditions distribute various kinds of bound orbits in different regions of the ($E$, $L$) and ($e$, $\mu$) planes, depending on which pair of roots of the effective potential forms a bound orbit. We provide a prescription to select these parameters for bound orbits, which are useful inputs to study bound trajectory evolution in various astrophysical applications like simulations of gravitational wave emission from extreme-mass ratio inspirals, relativistic precession around black holes, and the study of gyroscope precession as a test of general relativity.

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Prerna Rana, A. Mangalam. 2022-07-12. Bound orbit domains in the phase space of the Kerr geometry. https://doi.org/10.1142/9789811258251_0116

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