Gravitational self force theory provides a leading framework for modelling gravitational wave emission from compact binaries with asymmetric mass ratios. In this approach, the spacetime metric is expanded perturbatively in powers of the mass ratio. Traditional frequency domain implementations employ variation of parameters techniques and solve the field equations on constant time hypersurfaces, with boundary conditions imposed at finite radius via series expansions of the asymptotic solutions. While highly successful, this strategy requires delicate boundary condition matching and is poorly suited to non-compact sources, for which homogeneous solutions must be constructed over the entire radial domain. This issue becomes especially acute in second-order self-force calculations.
More recently, a new approach has emerged in which the spacetime is foliated by horizon penetrating hyperboloidal slices [Phys. Rev. D 105, 104033], and the radial coordinate is compactified along these surfaces. This geometric reformulation enables a natural treatment of infinity and the event horizon within a finite computational domain and eliminates the need for artificial outer boundary conditions. In this talk, I shall present applications of this framework to gravitational perturbations in the Lorenz gauge, focusing on both first- and second-order self force calculations. The method is shown to be accurate and computationally efficient at first-order, while also providing a viable route towards practical second-order implementations.