Separating the linearized Einstein equations in the background of a Kerr black hole

Abstract

The advancement in gravitational wave detection has made it possible to study the nonlinear effects in black hole perturbations, the modeling of which requires the full knowledge of the linear order perturbation of the metric. For the most interesting Kerr background, the conventional practice is to solve the Teukolsky equations for a Weyl scalar, and then the perturbation of the metric components is obtained using an elaborated metric reconstruction scheme, which, however, comes with unwanted restrictions. So it is desirable to separate the linearized Einstein equations in Kerr directly, i.e., without using metric reconstruction. In this work, I present a method that aims to help achieve this goal.