Extending second-order self-force calculations to Kerr spacetime

Black hole perturbation theory has recently offered exciting progress in modelling the binary problem using the self-force approach. First-post adiabatic self-force waveforms for quasi-circular inspirals in Schwarzschild spacetime have shown remarkable agreement with Numerical Relativity, even in the 1:10 mass ratio regime. The dissipative second-order self-force is a crucial contribution to these waveforms. However, extending second-order calculations to Kerr spacetime offers many barriers. This talk presents my progress in overcoming some of these barriers. I discuss how multiple second-order Teukolsky equations exist, how to make their sources well-defined in the self-force problem, and how to avoid divergences. One key advantage of the Teukolsky equation is its separability. However, the lack of symmetry of the Kerr metric seemingly prevents the separability of generic Teukolsky sources without expensive numerical calculations. I present a method for analytically separating generic sources in Kerr spacetime to a given accuracy.