Gravitational perturbations of rotating black holes in Lorenz gauge

TL;DR

This paper develops Lorenz-gauge solutions for gravitational perturbations of Kerr black holes, expressing them through homogeneous Teukolsky solutions and additional mass and angular momentum perturbations, applicable to Petrov type-D spacetimes.

Contribution

It introduces a method to construct full metric perturbations in Lorenz gauge from Teukolsky solutions, including mass and angular momentum perturbations, for Kerr spacetime.

Findings

Derived Lorenz-gauge solutions from Teukolsky equations.

Included perturbations to mass and angular momentum.

Applicable to Petrov type-D spacetimes with conformal Killing-Yano tensor.

Abstract

Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations. However, for certain applications it is desirable to construct the full metric perturbation in the Lorenz gauge, in which the linearized Einstein field equations take a manifestly hyperbolic form. Here we obtain a set of Lorenz-gauge solutions to the vacuum field equations in terms of homogeneous solutions to the spin-2, spin-1 and spin-0 Teukolsky equations; and completion pieces that represent perturbations to the mass and angular momentum of the spacetime. The solutions are valid in vacuum Petrov type-D spacetimes that admit a conformal Killing-Yano tensor.