Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails

We develop a complete and systematic analytical approach to field perturbations of extremal Kerr spacetime based on the formalism of Mano, Suzuki and Takasugi (MST) for the Teukolsky equation. Analytical expressions for the radial solutions and frequency-domain Green function in terms of infinite series of special functions are presented. As an application, we compute the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbationson and off the event horizon