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H 1 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)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 13/07/17
      Date de captation : 06/07/17
      Collection : Partial Differential Equations ; Mathematical Physics
      Sous collection : Research talks
      Format : MP4
      Domaine : PDE ; Mathematical Physics
      Durée : 00:51:05
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-07-06_Huneau.mp4

    Informations sur la rencontre

    Nom de la rencontre : Asymptotic analysis of evolution equations / Analyse asymptotique des équations d'évolution
    Organisateurs de la rencontre : Burq, Nicolas ; Delort, Jean-Marc ; Gérard, Patrick ; Koch, Herbert ; Thomann, Laurent
    Dates : 03/07/17 - 07/07/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1546.html

    Citation Data

    DOI : 10.24350/CIRM.V.19192803
    Cite this video as: Huneau, Cécile (2017). High frequency back reaction for the Einstein equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19192803
    URI : http://dx.doi.org/10.24350/CIRM.V.19192803

    Voir aussi


    1. Huneau, C., & Luk, J. (2017). High-frequency backreaction for the Einstein equations under polarized $\mathbb{U}(1)$ symmetry. - https://arxiv.org/abs/1706.09501

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