Late-Time Decay of Scalar Perturbations Outside Rotating Black Holes

We present an analytic method for calculating the late-time tails of a linear scalar field outside a Kerr black hole. We give the asymptotic behavior at timelike infinity (for fixed $r$), at future null-infinity, and along the event horizon (EH). In all three asymptotic regions we find a power-law decay. We show that the power indices describing the decay of the various modes at fixed $r$ differ from the corresponding Schwarzschild values. Also, the scalar field oscillates along the null generators of the EH (with advanced-time frequency proportional to the mode's magnetic number $m$).