"Flux-balance formulae" for extreme mass-ratio inspirals.

The "flux-balance formulae" that determine the averaged evolution of energy, azimuthal angular momentum and Carter constant in terms of the averaged asymptotic gravitational-wave fluxes for inspirals of small bodies into Kerr black holes were first derived about 15 years ago. However, this derivation is restricted to the case that the background Kerr geodesics are non-resonant (i.e., the radial and angular motions are always incommensurate), and excludes the resonant case that can be important for the radiative dynamics of the extreme mass-ratio inspirals. We here give a new derivation of the flux formulae based on Hamiltonian dynamics of a self-forced particle motion, which is a valuable tool for analyzing self-force effects on generic (eccentric, inclined) bound orbits in the Kerr spacetime. This Hamiltonian derivation using action-angle variables is much simpler than the previous one, applies to the resonant inspirals without any complication, and can be straightforwardly implemented by using the analytical/numerical Teukolsky-based flux codes.