Regularization of the Teukolsky equation for rotating black holes

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 the Poisson approach to regularize the nonrotating 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.