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

TL;DR

This paper presents a new Hamiltonian-based derivation of flux-balance formulae for extreme mass-ratio inspirals, extending applicability to resonant orbits and simplifying previous methods, aiding gravitational-wave modeling.

Contribution

A novel Hamiltonian derivation of flux formulae that includes resonant orbits and simplifies analysis of self-forced motion in Kerr spacetime.

Findings

Derivation applicable to resonant and non-resonant orbits.

Simpler Hamiltonian approach using action-angle variables.

Compatible with existing flux computation codes.

Abstract

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 extreme mass-ratio inspirals. We give here 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 resonant inspirals without any complication, and can be straightforwardly implemented by using analytical/numerical Teukolsky-based flux codes.