  We study analytically, via the Newman-Penrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as well as at null infinity and along the event horizon (EH). For generic initial data we derive the power-law indices for all radiating modes of the various fields. We also give an exact analytic expression (accurate to leading order in 1/t) for the r-dependence of the late time tail at any r. Some of our main conclusions are: (i) For generic initial data, the late time behavior of the fields is dominated by the mode l=|s| (with s being the spin parameter), which dies off at fixed $r$ as $t^{-2|s|-3}$ --- as in the Schwarzschild background. (ii) However, other modes admit decay rates slower than in the Schwarzschild case. (iii) For s>0 fields, non-axially symmetric modes dominate the late time behavior along the EH. These modes oscillate along the null generators of the EH. 
Late time decay of scalar, electromagnetic, and gravitational   perturbations outside rotating black holes