Calculating the second-order self-force for a Teukolsky formalism

Second-order self-force calculations are crucial to modelling extreme mass-ratio inspirals (EMRIs) and recently have been shown to also model intermediate mass-ratio binaries (IMRIs). These calculations are carried out in the Lorenz gauge, which is not separable in the astrophysical relevant scenario of Kerr spacetime. Hence we are now pursuing a second-order calculation for the Teukolsky equation. In this talk, I present a numerical implementation to compute the second-order Weyl scalar with a new, alternative hyperboloidal method. In this approach, the spacetime is foliated by horizon-penetrating hyperboloidal slices. Further compactifying the coordinates along these slices allows for simple treatment of the boundary conditions and implementing this approach with a multi-domain spectral solver. We shall consider preliminary results for the second-order flux from applying this method with an appropriately constructed second-order source for quasi-circular orbits in Schwarzschild spacetime.