Speaker : S. Isoyama

Title : Hamiltonian formulation of self-forced motion in Kerr : conservative dynamics

Abstract : With application to compact binaries in the large mass-ratio regime, the foundation and the implementation of self-force theory have now reached maturity. Despite that, the self-forced motion depends on one’s choice of gauge, hence we still need to learn how to practically devise gauge-invariant observables that describe post-geodesic corrections to the orbital dynamics. To this end, Kyoto group has initiated to formulate self-forced motion in Kerr as a 4-dimensional Hamiltonian-like dynamics. In this talk, we discuss the generic (i.e., eccentric and inclined) orbital dynamics under the conservative part of the linear self-force from the view point of our Hamiltonian formulation. Given a fixed metric perturbation generated by a fixed source orbit, we firstly show that the orbital-averaged redshift and frequencies are gauge-invariant characterization of the dynamical orbit. Making use of the gauge freedom in motion, we then show that the dynamical orbit is described by the single integral Hamiltonian in a certain gauge, irrespective of the source orbit of self force. Along the way, we also present several applications of our integrable Hamiltonian to demonstrate how our approach is useful to calculate observable effects of conservative self-force. This includes a frequency shift of the innermost stable (inclined) circular orbit and "a first law of binary mechanics" for generic orbits.