Perturbation Method for Classical Spinning Particle Motion: I. Kerr Space-Time

TL;DR

This paper develops an analytic perturbation method to study the motion of a classical spinning particle in Kerr spacetime, revealing how spin-curvature coupling affects particle dynamics, mass, and spin, especially near the black hole horizon.

Contribution

It introduces a general perturbation formalism for spinning particles in Kerr spacetime, including explicit formulas and analysis of mass and spin shifts due to spin-curvature effects.

Findings

Mass and spin of the particle can shift due to spin-curvature coupling.

Explicit expressions for circular orbits near the Kerr horizon are derived.

Preliminary stability analysis of spinning particle orbits is presented.

Abstract

This paper presents an analytic perturbation approach to the dynamics of a classical spinning particle, according to the Mathisson-Papapetrou-Dixon (MPD) equations of motion, with a direct application to circular motion around a Kerr black hole. The formalism is established in terms of a power series expansion with respect to the particle's spin magnitude, where the particle's kinematic and dynamical degrees are expressed in a completely general form that can be constructed to infinite order in the expansion parameter. It is further shown that the particle's squared mass and spin magnitude can shift due to a classical analogue of radiative corrections that arise from spin-curvature coupling. Explicit expressions are determined for the case of circular motion near the event horizon a Kerr black hole, where the mass and spin shift contributions are dependent on the initial conditions of the particle's spin orientation. A preliminary analysis of the stability properties of the orbital motion in the Kerr background due to spin-curvature interactions is explored and briefly discussed.