  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.

General Relativity and Quantum Cosmology