Gravitational perturbations of rotating black holes in Lorenz gauge

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.

6 pages, no figures. Version accepted by PRL

References in corpus (5)

• xPerm: fast index canonicalization for tensor computer algebra
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Maxwell's Equations in the Myers-Perry Geometry
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• New metric reconstruction scheme for gravitational self-force calculations

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• Probing fundamental physics with Extreme Mass Ratio Inspirals: a full Bayesian inference for scalar charge
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations
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• Sourced metric perturbations of Kerr spacetime in Lorenz gauge
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• Spin-2 Green's Functions on Kerr in Radiation Gauge
• Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
• Constants of motion in gravitational self-force theory
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• Frequency-domain self-force calculations using Gegenbauer reconstruction