Perturbations of a Schwarzschild black hole. Notes on Zerilli's approach

Modelling the free fall (and radiative phenomenology) of a massive particle, charged or not, in a static and spherically symmetric black hole is a classic, good relativistic dare that produced a remarkable series of papers, mainly in the seventies of the past century. Some formal topics about the mathematical machinery required to perform the task are unfortunately still not very clear; however, with the help of modern computer algebra techniques, some results can at least be tested and corrected.