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- W4383499304 abstract "We show the stability of the geometric optics approximation in general relativity by constructing a family $(g_lambda)_{lambdain(0,1]}$ of high-frequency metrics solutions to the Einstein vacuum equations in 3+1 dimensions without any symmetry assumptions. In the limit $lambdato 0$ this family approaches a fixed background $g_0$ solution of the Einstein-null dust system, illustrating the backreaction phenomenon. We introduce a precise second order high-frequency ansatz and identify a generalised wave gauge as well as polarization conditions at each order. The validity of our ansatz is ensured by a weak polarized null condition satisfied by the quadratic non-linearity in the Ricci tensor. The Einstein vacuum equations for $g_lambda$ are recast as a hierarchy of transport and wave equations, and their coupling induces a loss of derivatives. In order to solve it, we take advantage of a null foliation associated to $g_0$ as well as a Fourier cut-off adapted to our ansatz. The construction of high-frequency initial data solving the constraint equations is the content of our companion paper cite{Touati2023a}." @default.
- W4383499304 created "2023-07-08" @default.
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- W4383499304 date "2023-07-07" @default.
- W4383499304 modified "2023-10-18" @default.
- W4383499304 title "Geometric Optics Approximation for the Einstein Vacuum Equations" @default.
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- W4383499304 doi "https://doi.org/10.1007/s00220-023-04790-x" @default.
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