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

TL;DR

This paper revisits the perturbation theory of Schwarzschild black holes, clarifying mathematical methods and leveraging modern computer algebra to test and refine classical results from the 1970s.

Contribution

It provides new insights into Zerilli's approach and enhances the mathematical understanding of black hole perturbations using computational tools.

Findings

Clarified mathematical machinery for black hole perturbations

Tested and corrected classical results with computer algebra

Improved understanding of Zerilli's formalism

Abstract

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.