Gravitational Perturbations of Rotating Black Holes in Lorenz Gauge

Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of gauge 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 linearized vacuum field equations on Kerr-Newman-Unti-Tamburino spacetimes in terms of homogeneous solutions to the spin-2, spin-1, and spin-0 Teukolsky equations. We also derive Lorenz-gauge completion pieces representing mass and angular momentum perturbations of Kerr spacetime.