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arXiv · 2406.12510

Sourced metric perturbations of Kerr spacetime in Lorenz gauge

Barry Wardell·Chris Kavanagh·Sam R. Dolan
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Abstract

We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of six scalars, with two of spin-weight $\pm2$, two of spin-weight $\pm1$, and two of spin-weight $0$. We derive the sourced Teukolsky equations satisfied by these scalars, with the sources given in terms of differential operators acting on the stress-energy tensor. The method can be used to obtain both linear and higher order nonlinear metric perturbations, and it fully determines the metric perturbation up to a time integral, omitting only static contributions which must be handled separately.

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Barry Wardell, Chris Kavanagh, Sam R. Dolan. 2024-06-18. Sourced metric perturbations of Kerr spacetime in Lorenz gauge. https://doi.org/10.1088/1361-6382%2Fae0918

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