Near-Horizon Kerr Perturbations
This work builds a horizon-side formulation for gravitational perturbations of rotating black holes. The key problem is practical as much as formal: the spin-weight (s=+2) source term is the natural object near the horizon, but its direct expression is hard to evaluate stably for generic EMRI orbits. We reorganize the source into a convergent form and use it to compute shear perturbations and horizon fluxes.
In short, the project does three things:
- constructs a numerically stable source for near-horizon (s=+2) Kerr perturbations;
- computes the corresponding shear perturbation and flux for generic orbits;
- checks the result against the Teukolsky calculation, so the horizon-side and infinity-side descriptions are tied to the same physical perturbation.
The conclusion is that the near-horizon formulation is not just a formal rewriting. It gives a stable numerical route to horizon observables, and it also fixes conventions that are useful for the shared Y variable used in the Generalized Sasaki-Nakamura infrastructure.
The implementation is part of GeneralizedSasakiNakamura.jl.