Gravitational Perturbations of the Kerr black hole due to arbitrary sources

TL;DR

This paper develops a formalism to describe gravitational perturbations of Kerr black holes with arbitrary sources in horizon-penetrating coordinates, aiding the study of black hole interactions.

Contribution

It introduces a perturbative framework for Kerr black holes with arbitrary sources in horizon-penetrating coordinates, facilitating analysis of black hole evolution during close encounters.

Findings

Explicit derivation of field equations for perturbed Weyl scalars with sources.

Construction of null tetrads in Kerr-Schild coordinates.

Framework applicable to black hole merger and interaction studies.

Abstract

We describe the Kerr black hole in the ingoing and outgoing Kerr-Schild horizon penetrating coordinates. Starting from the null vector naturally defined in these coordinates, we construct the null tetrad for each case, as well as the corresponding geometrical quantities allowing us to explicitly derive the field equations for the ${\Psi_0}^{(1)}$ and ${\Psi_4}^{(1)}$ perturbed scalar projections of the Weyl tensor, including arbitrary source terms. This perturbative description, including arbitrary sources, described in horizon penetrating coordinates is desirable in several lines of research on black holes, and contributes to the implementation of a formalism aimed to study the evolution of the space time in the region where two black holes are close.