Extending Hamiltonian Formulation of Particle Motion in Perturbed Kerr Spacetime to various time parameterizations

TL;DR

This paper explores how different time parameterizations affect the Hamiltonian formulation of particle motion in perturbed Kerr spacetime, clarifying their interrelations for better modeling of gravitational wave sources.

Contribution

It extends the Hamiltonian formalism with action-angle variables to include various time parameterizations beyond proper time.

Findings

Clarifies relations between different orbit parameterizations.

Extends Hamiltonian formalism to alternative time variables.

Facilitates more flexible modeling of particle trajectories.

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.