LISA’s required phase precision can only be achieved by including second-order gravitational self-force effects. These require solving the Einstein equations at second order in the mass ratio, with the source term constructed from products of the first-order metric perturbation. Computing this source is one of the central technical challenges of the field: it diverges at the particle’s location and must be handled through carefully designed puncture schemes that capture the singular structure analytically.
We have produced the first complete second-order source for quasi-circular orbits in Schwarzschild and have used it to compute the post-adiabatic waveform corrections needed for LISA. Work is now under way to extend the framework to generic orbits — eccentric and inclined — and to the astrophysically relevant Kerr background, where the technical demands are substantially higher.
Current focus:
- Generic eccentric and inclined orbits in Schwarzschild
- Extension to Kerr backgrounds
- Integration of the second-order source into production numerical solvers
- Cross-validation against independent calculations