Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation - art. no. 044029

As shown by Teukolsky, the master equation governing the propagation of wea k radiation in a black hole spacetime can be separated into four ordinary d ifferential equations, one for each spacetime coordinate. ("Weak" means the radiation's amplitude is small enough that its own gravitation may be negl ected.) Unfortunately, it is difficult to accurately compute solutions to t he separated radial equation (the Teukolsky equation), particularly in a nu merical implementation. The fundamental reason for this is that the Teukols ky equation's potentials are long ranged. For nonspinning black holes, one can get around this difficulty by applying transformations which relate the Teukolsky solution to solutions of the Regge-Wheeler equation, which has a short-ranged potential. A particularly attractive generalization of this a pproach to spinning black holes for gravitational radiation (spin weight s= -2) was given by Sasaki and Nakamura. In this paper, 1 generalize the Sasak i-Nakamura results to encompass radiation fields of arbitrary integer spin weight, and give results directly applicable to scalar (s=0) and electromag netic (s=-1) radiation. These results may be of interest for studies of ast rophysical radiation processes near black holes, and of programs to compute radiation reaction forces in curved spacetime.