Gravitational Self-Force with Hyperboloidal Slicing

Explore gravitational self-force theory through a novel hyperboloidal slicing approach in this 27-minute conference lecture. Learn how this leading framework models gravitational wave emission from compact binaries with asymmetric mass ratios by expanding the spacetime metric perturbatively in powers of the mass ratio. Discover the limitations of traditional frequency domain implementations that use variation of parameters techniques on constant time hypersurfaces, including challenges with boundary condition matching and difficulties with non-compact sources, particularly in second-order self-force calculations. Examine the innovative hyperboloidal foliation method that uses horizon-penetrating slices with compactified radial coordinates, enabling natural treatment of infinity and event horizons within finite computational domains while eliminating artificial outer boundary conditions. Analyze applications to gravitational perturbations in the Lorenz gauge, covering both first- and second-order self-force calculations, and understand how this geometric reformulation provides accuracy, computational efficiency, and a viable pathway for practical second-order implementations in gravitational wave physics.