"Hamiltonian" Dynamics of Self-Forced Motion in Kerr Spacetime

Gravitational waves observations from compact objects inspiralling into massive black holes are  promising targets to test GR in strong field regime. When the mass ratio is small, the problem admits a perturbative description, where the corrections to the geodesic motion of the smaller object are best handled by the notion of a gravitational self-force. In this talk, we propose a "Hamiltonian" formulation of the self-force dynamics in Kerr spacetime, which describes the binary dynamics linear order in mass ratio in terms of a geodesic motion in a certain locally defined effective smooth spacetime. Our formulation uses action-angle variables to respect the integrability of the Kerr geodesics motion, and gives a significantly simplified method to compute the post-geodesic motion in Kerr spacetime. For the conservative dynamics, we show that our Hamiltonian is effectively "integrable", and present the recent calculation of a the frequency shift of the inner most stable circular orbit in Kerr spacetime due to the conservative self-force. We also sketch how we practically formulate the long-term inspiral dynamics, using the special choice of gauge.