As shown by Teukolsky , the master equation governing the propagation of weak radiation in a black hole spacetime can be separated into four ordinary differential equations , one for each spacetime coordinate .
( “ Weak ” means the radiation ’ s amplitude is small enough that its own gravitation may be neglected . )
Unfortunately , it is difficult to accurately compute solutions to the separated radial equation ( the Teukolsky equation ) , particularly in a numerical implementation .
The fundamental reason for this is that the Teukolsky equation ’ s potentials are long ranged .
For non-spinning 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 approach to spinning black holes for gravitational radiation ( spin weight s = -2 ) was given by Sasaki and Nakamura .
In this paper , I generalize Sasaki and Nakamura ’ s results to encompass radiation fields of arbitrary integer spin weight , and give results directly applicable to scalar ( s = 0 ) and electromagnetic ( s = -1 ) radiation .
These results may be of interest for studies of astrophysical radiation processes near black holes , and of programs to compute radiation reaction forces in curved spacetime .