Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?

摘要: A point-like object moving in a background black hole spacetime experiences gravitational self-force which can be expressed as local function of the object's instantaneous position and velocity, to linear order mass ratio. We consider worldline dynamics defined by conservative part self-force, turning off dissipative part, we ask: Is that dynamical system Hamiltonian system, if so, is it integrable? In Schwarzschild spacetime, show integrable, ratio, for generic (but not necessarily all) stable bound orbits. There exist an energy angular momentum, being perturbed versions their counterparts geodesic motion, are conserved under forced motion. also discuss difficulties associated with establishing analogous results Kerr spacetime. This result may useful future computational schemes, based on description, calculating its observable effects. It relevant assumption existence orbits effective-one-body formalism, but all orders post-Newtonian expansion.