How do black holes ring as they settle down?

Quasinormal modes are the characteristic 'ringdown' frequencies a black hole emits after a perturbation — the signal LIGO hears after a merger. Near spacelike infinity, the equations governing these modes become too irregular for exact solutions. Applying Poincaré asymptotic expansions — a tool from 1886 — the authors show you can compute the radial field behavior there to arbitrary precision, offering a cleaner path to quasinormal mode calculations in Petrov-D spacetimes like Kerr.