Around the bounded L 2 curvature conjecture in general relativity

Sergiu Klainerman[1]; Igor Rodnianski[1]; Jeremie Szeftel[2]

  • [1] Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA
  • [2] Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA and Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex FRANCE

Journées Équations aux dérivées partielles (2008)

  • Volume: 202, Issue: 1, page 1-15
  • ISSN: 0752-0360

Abstract

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We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation □ g φ = 0 , where ≫ is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L 2 bounds on the curvature tensor R of ≫ is a major step towards the proof of the bounded L 2 curvature conjecture.

How to cite

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Klainerman, Sergiu, Rodnianski, Igor, and Szeftel, Jeremie. "Around the bounded $L^2$ curvature conjecture in general relativity." Journées Équations aux dérivées partielles 202.1 (2008): 1-15. <http://eudml.org/doc/10641>.

@article{Klainerman2008,
abstract = {We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation $\square _\{\bf g\} \phi =0$, where $\gg $ is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes $L^2$ bounds on the curvature tensor $\{\bf R\}$ of $\gg $ is a major step towards the proof of the bounded $L^2$ curvature conjecture.},
affiliation = {Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA; Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA; Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA and Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex FRANCE},
author = {Klainerman, Sergiu, Rodnianski, Igor, Szeftel, Jeremie},
journal = {Journées Équations aux dérivées partielles},
keywords = {Einstein vacuum equations; curvature bounds; causal geometry; quasilinear hyperbolic systems; radius of injectivity},
language = {eng},
month = {6},
number = {1},
pages = {1-15},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Around the bounded $L^2$ curvature conjecture in general relativity},
url = {http://eudml.org/doc/10641},
volume = {202},
year = {2008},
}

TY - JOUR
AU - Klainerman, Sergiu
AU - Rodnianski, Igor
AU - Szeftel, Jeremie
TI - Around the bounded $L^2$ curvature conjecture in general relativity
JO - Journées Équations aux dérivées partielles
DA - 2008/6//
PB - Groupement de recherche 2434 du CNRS
VL - 202
IS - 1
SP - 1
EP - 15
AB - We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation $\square _{\bf g} \phi =0$, where $\gg $ is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes $L^2$ bounds on the curvature tensor ${\bf R}$ of $\gg $ is a major step towards the proof of the bounded $L^2$ curvature conjecture.
LA - eng
KW - Einstein vacuum equations; curvature bounds; causal geometry; quasilinear hyperbolic systems; radius of injectivity
UR - http://eudml.org/doc/10641
ER -

References

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