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

TL;DR

This paper develops an analytical framework for studying field perturbations in extremal Kerr spacetime, providing explicit solutions and analyzing late-time tail behavior for scalar, electromagnetic, and gravitational fields.

Contribution

It introduces a systematic MST-based method to compute radial solutions and Green functions, and for the first time determines late-time decay tails in extremal Kerr.

Findings

Derived explicit radial solutions using MST formalism.

Computed late-time decay tails for various field perturbations.

Confirmed consistency of Green function behavior near superradiant bound frequency.

Abstract

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, for the first time, the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbations on and off the event horizon. We also use the MST method to compute the leading behavior of the Green function modes near the branch point at the superradiant bound frequency and show that this behavior agrees with existing results in the literature using a different method.