Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin

TL;DR

This paper demonstrates that the motion of a spinning particle under the conservative self-force in a stationary spacetime can be described by a Hamiltonian system to first order in mass and spin, extending previous spinless results.

Contribution

It introduces a Hamiltonian formulation for spinning particles under conservative self-force, incorporating spin effects to linear order, extending prior spinless models.

Findings

The perturbed system remains Hamiltonian with explicit Hamiltonian and symplectic form expressions.

The approach generalizes previous spinless particle models to include spin effects.

The results facilitate analysis of spinning particle dynamics in curved spacetime.

Abstract

We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the Mathisson-Papapetrou-Dixon equations of motion with the Tulczyjew-Dixon spin supplementary condition, to linear order in spin. We then perturb this system by adding the conservative pieces of the leading order gravitational self-force and self-torque sourced by the particle's mass and spin. We show that this perturbed system is Hamiltonian and derive expressions for the Hamiltonian function and symplectic form. This result extends our previous result for spinless point particles.