Metric perturbations of Kerr spacetime 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. Directly solving the Lorenz gauge equations in Kerr spacetime is challenging for two reasons: (i) unlike the Teukolsky equation, the Lorenz gauge equations are not known to admit separable solutions; (ii) the equations for the ten components of the metric perturbation are coupled. In this talk, I will present a formalism in which the Lorenz gauge metric perturbation is obtained from a set of six decoupled and separable solutions to the spin-2, spin-1 and spin-0 Teukolsky equations. The formalism is ideally suited to hyperboloidal methods, which have been shown to provide a highly-efficient approach to solving Teukolsky equations. As a demonstration of the approach, I will give results for the Lorenz-gauge gravitational self-force problem in Kerr spacetime. This talk is based on work with Sam Dolan, Chris Kavanagh and Leanne Durkan.