Fully separated metric perturbations over the Kerr background

TL;DR

This paper introduces two fully separated solutions to metric perturbation equations over the Kerr background, advancing the analysis of gravitational waves and black hole perturbations.

Contribution

It provides the first direct, fully separated solutions to metric perturbations in Kerr spacetime, bypassing the need for metric reconstruction from Weyl scalars.

Findings

Two complementary solutions to metric perturbation equations are derived.

The solutions enable direct analysis of Kerr black hole perturbations.

This work simplifies the study of gravitational waves in Kerr backgrounds.

Abstract

The advancement in gravitational wave detection has made it necessary to study the nonlinear effects in black hole perturbation theory. For the most interesting Kerr background, the current basis of the study, the Teukolsky equation, is given in terms of the Weyl scalars and elaborated metric reconstruction schemes are needed to obtain the full metric perturbation. In this work, I present two complementary and fully separated solutions to the metric perturbation equations directly.