Separating metric perturbations in near-horizon extremal Kerr

Understand

Linear perturbation theory is a powerful toolkit for studying black hole spacetimes.

• However, the perturbation equations are hard to solve unless we can use separation of variables.
• In the Kerr spacetime, metric perturbations do not separate, but curvature perturbations do.
• The cost of curvature perturbations is a very complicated metric-reconstruction procedure.