Regularization of the Teukolsky Equation for Rotating Black Holes

TL;DR

This paper develops a method to regularize the radial Teukolsky equation for rotating black holes, enabling well-behaved solutions for sources extending to infinity, which is crucial for gravitational wave modeling.

Contribution

It extends Poisson's regularization approach from non-rotating to rotating black holes using Chandrasekhar transformations, improving solution regularity for the Teukolsky equation.

Findings

Successfully regularized the Teukolsky equation with extended sources

Extended Poisson's approach to rotating black holes

Provided a framework for well-behaved solutions in gravitational wave calculations

Abstract

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.