Parametric solutions to the Kerr separatrix

TL;DR

This paper derives explicit parametric solutions for the Kerr separatrix boundary in black hole spacetime, improving understanding of orbit stability and transitions.

Contribution

It introduces a new method to explicitly parametrize the Kerr separatrix using unstable spherical orbit radii, extending previous polynomial solutions.

Findings

Explicit solutions parametrized by unstable spherical orbit radius

Extension of previous polynomial equations for the separatrix

Enhanced understanding of orbit boundaries in Kerr spacetime

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.