  We show that the radial Teukolsky equation (in the frequency domain) with
sources that extend to infinity has well-behaved solutions. To prove that, we
follow Poisson approach to regularize the non-rotating hole, and extend it to
the rotating case. To do so we use the Chandrasekhar transformation among the
Teukolsky and Regge-Wheeler-like equations, and express the integrals over the
source in terms of solutions to the homogeneous Regge-Wheeler-like equation, to
finally regularize the resulting integral. We then discuss the applicability of
these results.
