A pseudo-Hamiltonian reformulation of 1PA self-force dynamics yields local, invariant action-angle evolution equations and an embedded conservative Hamiltonian whose on-shell energy equals the first-law binding energy.
Extending Hamiltonian Formulation of Particle Motion in Perturbed Kerr Spacetime to various time parameterizations
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abstract
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory is considered to be appropriate when developing formal arguments, but these arguments can easily be extended to arguments with other time variables. The aim of this paper is to clarify the relations between the schemes with various parameterizations of the orbit.
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Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
A pseudo-Hamiltonian reformulation of 1PA self-force dynamics yields local, invariant action-angle evolution equations and an embedded conservative Hamiltonian whose on-shell energy equals the first-law binding energy.