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arXiv · 2502.18141

Parametric solutions to the Kerr separatrix

Tammy Ng·Edward Teo
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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.

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Tammy Ng, Edward Teo. 2025-02-25. Parametric solutions to the Kerr separatrix. https://doi.org/10.1088/1361-6382/adba36

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