Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes
Abstract
We study analytically, via the NewmanPenrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a powerlaw decay at timelike infinity, as well as at null infinity and along the event horizon (EH). For generic initial data we derive the powerlaw 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 the following. (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, nonaxially symmetric modes dominate the late time behavior along the EH. These modes oscillate along the null generators of the EH.
 Publication:

Physical Review D
 Pub Date:
 December 1999
 DOI:
 10.1103/PhysRevD.61.024026
 arXiv:
 arXiv:grqc/9908005
 Bibcode:
 1999PhRvD..61b4026B
 Keywords:

 04.70.Bw;
 04.25.Nx;
 Classical black holes;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 General Relativity and Quantum Cosmology
 EPrint:
 48 pages, REVTeX