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Journal Article

Taming the Nonlinearity of the Einstein Equation

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

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Fulltext (public)

PhysRevLett.113_261103.pdf
(Any fulltext), 123KB

1409.4674v2.pdf
(Preprint), 136KB

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Citation

Harte, A. I. (2014). Taming the Nonlinearity of the Einstein Equation. Physical Review Letters, 113(26): 261103. doi:10.1103/PhysRevLett.113.261103.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-9425-1
Abstract
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein’s equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein’s equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.