Parametric solutions to the Kerr separatrix
arXiv:2502.18141 · doi:10.1088/1361-6382/adba36
Abstract
The Kerr separatrix is a boundary in parameter space that separates bound orbits from plunging orbits in the Kerr black hole space-time. Recently, Stein and Warburton found a polynomial equation for the location of the separatrix, for two different choices of inclination parameter. Following a method of Levin and Perez-Giz developed for the equatorial case, we use a correspondence between homoclinic orbits and unstable spherical orbits to derive explicit solutions to the separatrix polynomials. These solutions are parametrised in terms of the radius of the unstable spherical orbit.
arXiv comment12 pages, accepted for publication in Classical and Quantum Gravity
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