Geodesic
Geometric optics approximation for the Einstein vacuum equations
Touati, Arthur1
1 Institut des Hautes Études Scientifiques 91440 Bures-sur-Yvette, France
Séminaire Laurent Schwartz — EDP et applications (2022-2023), Exposé no. 7, 13 p.

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We present recent works on the construction of high-frequency solutions to the Einstein vacuum equations in general relativity, based on [Tou22b, Tou23]. In these articles, the author shows the existence of a family of vacuum spacetimes (g λ ) λ∈(0,1] in generalised wave gauge oscillating at frequency λ -1 and defined by a geometric optics ansatz. In this survey, we first review the Cauchy theory for the Einstein vacuum equations in wave gauge, geometric optics and Burnett’s conjecture in general relativity. This will motivate our main result, for which we provide a sketch of proof high-lighting both quasi-linear and semi-linear challenges.

Publié le :
DOI : 10.5802/slsedp.159

Touati, Arthur 1

1 Institut des Hautes Études Scientifiques 91440 Bures-sur-Yvette, France 
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     title = {Geometric optics approximation for the {Einstein} vacuum equations},
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     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
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Touati, Arthur. Geometric optics approximation for the Einstein vacuum equations. Séminaire Laurent Schwartz — EDP et applications (2022-2023), Exposé no. 7, 13 p.. doi: 10.5802/slsedp.159

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