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Geometric optics approximation for the Einstein vacuum equations
Arthur Touati1
1 Institut des Hautes Études Scientifiques 91440 Bures-sur-Yvette, France
Séminaire Laurent Schwartz — EDP et applications (2022-2023), Talk no. 7, 13 p.
  • Abstract

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.

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Published online: 2023-07-12
DOI: 10.5802/slsedp.159
Author's affiliations:
Arthur Touati 1

1 Institut des Hautes Études Scientifiques 91440 Bures-sur-Yvette, France
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@article{SLSEDP_2022-2023____A2_0,
     author = {Arthur Touati},
     title = {Geometric optics approximation for the {Einstein} vacuum equations},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:7},
     pages = {1--13},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2022-2023},
     doi = {10.5802/slsedp.159},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.159/}
}
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AU  - Arthur Touati
TI  - Geometric optics approximation for the Einstein vacuum equations
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:7
PY  - 2022-2023
SP  - 1
EP  - 13
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.159/
DO  - 10.5802/slsedp.159
LA  - en
ID  - SLSEDP_2022-2023____A2_0
ER  - 
%0 Journal Article
%A Arthur Touati
%T Geometric optics approximation for the Einstein vacuum equations
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:7
%D 2022-2023
%P 1-13
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.159/
%R 10.5802/slsedp.159
%G en
%F SLSEDP_2022-2023____A2_0
Arthur Touati. Geometric optics approximation for the Einstein vacuum equations. Séminaire Laurent Schwartz — EDP et applications (2022-2023), Talk no. 7, 13 p. doi : 10.5802/slsedp.159. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.159/
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