Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time

TL;DR

This paper demonstrates that the equations of motion for spinning particles in Kerr space-time can be made separable to linear order in spin by a specific shift, enabling explicit solutions similar to non-spinning cases.

Contribution

It introduces a method to recover separability of spinning particle equations in Kerr space-time to linear order in spin using a worldline shift based on hidden symmetries.

Findings

Separable equations of motion for spinning particles are obtained to linear order in spin.

Explicit closed-form solutions for spinning particle trajectories are derived.

The method enhances modeling of inspirals of rotating objects into black holes.

Abstract

The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show that separability of the equations of motion can be recovered to linear order in spin by a shift of the worldline derived with the use of the hidden symmetry of Kerr space-time. Consequently, the closed-form solution of the motion is expressed in a way closely analogous to the solution for spinless particles. This finding enriches the understanding of separability and integrability properties of the dynamics of test particles and fields in Kerr space-time and is particularly valuable for modeling inspirals of rotating compact objects into massive black holes.