contributed talk @ 33rd pcgm, ucsb

Finding metric perturbations in the Kerr spacetime typically involves a detour through curvature perturbations and then metric reconstruction, which is a complicated procedure. Meanwhile, separation of variables is possible in Schwarzschild because of the extra symmetry. We show that the same is true in the near-horizon extremal Kerr spacetime: the emergent additional symmetries allow for separation of variables by using a basis adapted to that symmetry. The separation turns the system of partial differential equations into one of ordinary differential equations over a compact domain, the polar angle. As a direct application of our method, we find the linearized metric deformations to the near-horizon extremal Kerr geometry as induced by two string-inspired corrections to general relativity: Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons gravity, in the decoupling limit.