Multi angle High frequency back reaction for the Einstein equations
Auteurs : Huneau, Cécile (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tensor in the equation for the background metric. This non trivial contribution is of due to the nonlinearities in Einstein equations, which involve products of derivatives of the metric. It has been conjectured by Burnett that the only tensors which can be obtained this way are massless Vlasov, and it has been proved by Green and Wald that the limit tensor must be traceless and satisfy the dominant energy condition. The known exemples of this phenomena are constructed under symmetry reductions which involve two Killing fields and lead to an energy impulsion tensor which consists in at most two dust fields propagating in null directions. In this talk, I will explain our construction, under a symmetry reduction involving one Killing field, which leads to an energy impulsion tensor consisting in N dust fields propagating in arbitrary null directions. This is a joint work with Jonathan Luk (Stanford).Codes MSC :
35Q75 - PDEs in connection with relativity and gravitational theory
53C80 - Applications of global differential geometry to physics
83C05 - Einstein's equations (general structure, canonical formalism, Cauchy problems)