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Generating exact solutions to Einstein's equation using linearized approximations

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Harte,  Abraham I.
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Vines,  Justin
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1608.04359.pdf
(Preprint), 768KB

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Citation

Harte, A. I., & Vines, J. (2016). Generating exact solutions to Einstein's equation using linearized approximations. Physical Review D, 94: 084009. doi:10.1103/PhysRevD.94.084009.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-3F36-4
Abstract
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.