Particle motion under the conservative piece of the self-force is Hamiltonian

TL;DR

This paper demonstrates that the conservative component of the self-force in a stationary spacetime induces Hamiltonian dynamics for a point particle, extending previous results to resonant orbits and discussing implications for black hole mechanics.

Contribution

It establishes that the conservative self-force component leads to a Hamiltonian formulation and provides an explicit Hamiltonian expression, generalizing prior work to resonant orbits in Kerr spacetime.

Findings

Conservative self-force induces Hamiltonian dynamics.

Explicit Hamiltonian expression derived for Kerr spacetime.

Generalization to resonant orbits beyond previous non-resonant results.

Abstract

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita et. al., which is valid only for non-resonant orbits. We discuss implications for the first law of binary black hole mechanics.