Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes - art. no. 024026

We study analytically, via the Newman-Penrose formalism, the late time deca y of scalar, electromagnetic, and gravitational perturbations outside a rea listic rotating (Kerr) black hole. We find a power-law decay at timelike in finity, as well as at null infinity and along the event horizon (EH). For g eneric 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 an y r. Some of our main conclusions are the following. (i) For generic initia l 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 deca y rates slower than in the Schwarzschild case. (iii) For s>0 fields, non-ax ially symmetric modes dominate the late time behavior along the EH. These m odes oscillate along the null generators of the EH.