Non-axial angular momentum fluxes and black hole perturbation theory

Motivated largely by the need to develop accurate models for extreme mass ratio inspirals that will be measured by the planned LISA mission, there has been great progress in recent years modeling binaries in which one member is far more massive than the other. In the adiabatic limit, the action of the dissipative self-force which drives the evolution of such a system is equivalent to using simple ``flux-balancing’’ results, describing how a geodesic’s energy, axial angular momentum, and Carter constant change due to gravitational wave backreaction. A clear calculation of the non-axial components of angular momentum carried by gravitational waves has recently appeared in the literature. We demonstrate that, at least for a small body orbiting a Schwarzschild black hole, this calculation takes a particularly simple form by re-organizing the terms into the action of the spin-weighted spherical harmonic raising and lowering operators acting on curvature scalars. We apply this result to fluxes computed using black hole perturbation theory. We then discuss the groundwork for extending these calculations first to slowly rotating black holes and then to general Kerr holes, as well as potential applications of this framework to other problems in black hole perturbation theory.