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General Relativity and Quantum Cosmology, gr-qc
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.
