Gravitational radiation from infall into a black hole: Regularization of the Teukolsky equation

TL;DR

This paper demonstrates that the divergences in the Teukolsky equation for gravitational radiation from infalling matter are due to an incorrect Green's function choice, and presents a natural regularization method without modifying the original equation.

Contribution

It shows that the divergences are caused by Green's function choice and introduces a regularization method that preserves the original Teukolsky equation.

Findings

Divergences stem from Green's function choice

Regularization can be achieved without modifying the Teukolsky equation

Provides a natural, consistent approach to handle non-compact sources

Abstract

The Teukolsky equation has long been known to lead to divergent integrals when it is used to calculate the gravitational radiation emitted when a test mass falls into a black hole from infinity. Two methods have been used in the past to remove those divergent integrals. In the first, integrations by parts are carried out, and the infinite boundary terms are simply discarded. In the second, the Teukolsky equation is transformed into another equation which does not lead to divergent integrals. The purpose of this paper is to show that there is nothing intrinsically wrong with the Teukolsky equation when dealing with non-compact source terms, and that the divergent integrals result simply from an incorrect choice of Green's function. In this paper, regularization of the Teukolsky equation is carried out in an entirely natural way which does not involve modifying the equation.