Bound orbit domains in the phase space of the Kerr geometry

Abstract

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerrblack 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,μ,a,Q). These conditions distribute various kinds of bound orbitsin different regions of the (E,L)and(e,μ) planes, depending on which pair of rootsof the effective potential forms a bound orbit. We provide a prescription to select theseparameters for bound orbits, which are useful inputs to study bound trajectory evolutionin various astrophysical applications like simulations of gravitational wave emission fromextreme-mass ratio inspirals, relativistic precession around black holes, and the study ofgyroscope precession as a test of general relativity