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 held 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). [S0031-9007(99)09261-3].