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

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.

arXiv comment6 pages

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• Flux-balance laws for spinning bodies under the gravitational self-force
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• On the integrability of extended test body dynamics around black holes
• Dirac brackets for classical radiative observables
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• The first law of binary black hole scattering
• Flux-balance laws in scalar self-force theory
• Constants of motion in gravitational self-force theory