ºÚÁÏÉç

The self-force theory describes motion of a small body in a curved spacetime, including the back-reaction of its own gravitational field to the motion. With the future gravitational observation of large-mass-ratio compact binaries (stellar compact objects and a super massive black holes), the foundation of the self-force theory has reached maturity. So, the next step is concrete computation of self-force effects in astrophysical Kerr spacetime, using a convenient and practical scheme for implementation. Hamiltonian formulation of the self-force theory is one of such schemes. In Kerr spacetime, the geodesic Hamiltonian system is integrable. This property enables Hamiltonian formulation to provide simple scheme and a novel perspective of self-forced dynamics in Kerr spacetime. This talk provides an overview of our formulation. We will discuss its basics and conservative dynamics including several applications. We also sketch a multi-scale analysis of our Hamiltonian system to track the long-term dynamics of a small body.