Deriving the Separatrix for a Spinning Secondary on a Generic Kerr Orbit

The dynamics of a small body close to a massive black hole can be explored by identifying the location of the separatrix: the boundary in parameter space that separates stable and unstable (i.e., plunge) orbits. The separatrix is of particular importance for modeling gravitational wave emission from objects on extreme-mass-ratio inspiral trajectories. For non-spinning test masses on generic orbits, the location of the separatrix is well understood and can be expressed entirely in terms of the constants of motion of the orbits - total energy E, the z-component of the angular momentum L, and the Carter constant Q. Imparting a spin onto the test mass induces a self-force effect, pulling the particle away from geodesic motion. This project aims to solve for the location of the separatrix for a spinning secondary on a fully generic orbit around a massive Kerr black hole.