The nonlinear stability of the Minkowski metric in general relativity

  • D. Christodoulou
  • S. Klainerman
Hyperbolic P.D.E. Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1402)


Vector Field Minkowski Space Bianchi Identity Weyl Tensor Conformal Killing 
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  1. [Ba]
    R. Bartnik. Existence of maximal surfaces in asymptotically flat Space-Times. Math. Phys. 94, 1984, 155–175.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Bo]
    H. Bondi Nature 186, 1960, 535CrossRefGoogle Scholar
  3. [Bo-Bu-Me]
    H. Bondi-M.G.J. van der Burg-A.W.K. Metzner. Gravitational Waves in General Relativity vii. Proc. Roy. Soc. Lond. A269, 1962, 21–52.CrossRefzbMATHGoogle Scholar
  4. [Br]
    Y. Bruhat. Théorème d'existence pour certaines systèmes d'équations aux dérivées partielles non linéaires. Acta Mathematica 88 (1952), 141–225.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [Ch]
    D. Christodoulou. Global solutions for nonlinear hyperbolic equations for small data. Comm. Pure Appl. Math. 39, 1986, 267–282.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [Ch-Kl]
    D. Christodoulou-S. Klainerman. Asymptotic properties of linear field equations in Minkowski space. preprint.Google Scholar
  7. [Ch-Mu]
    D. Christodoulou-N. O'Murchadha. The Boost Problem in General Relativity. Comm. Math. Phys. 80, 1981, 271–300.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [Eisen]
    L.P.Eisenhart. Riemannian Geometry. Princeton University Press 1926.Google Scholar
  9. [Ho]
    L.Hörmander. On Sobolev spaces associated with some Lie Algebras. Report NO:4, Inst. Mittag-Leffler 1985.Google Scholar
  10. [Kl1]
    S. Klainerman. The null condition and global existence to nonlinear wave equations Lect. Appl. Math. 23, 1986, 293–326.MathSciNetzbMATHGoogle Scholar
  11. [Kl2]
    S. Klainerman. Remarks on the global Sobolev Inequalities in Minkowski Space. Comm. Pure Appl. Math. 40, 1987, 111–117.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [Kl3]
    S. Klainerman. Uniform decay estimates and the Lorentz invariance of the classical wave equation. Comm. Pure Appl. Math. 38, 1985, 321–332.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [Ne-To]
    E.T.Newman-K.P.Todd. Asymptotically flat space-times. General Relativity and Gravitation, vol 2, A. Held, Plenum. 1980Google Scholar
  14. [Pe1]
    R. Penrose. Structure of Space-Time. Battelle Rencontre. C.M.De Witt and J.A. Wheeler 1967Google Scholar
  15. [Pe2]
    R. Penrose. Zero rest mass fields including gravitation: Asymptotic Behaviour. Proc. Roy. Soc. Lond. A284, 1962, 159–203.MathSciNetzbMATHGoogle Scholar
  16. [Sa]
    R.K. Sacks Gravitational waves in General Relativity viii. Proc. Roy. Soc. Lond. A270, 1962, 103–126.CrossRefGoogle Scholar

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© Springer-Verlag 1989

Authors and Affiliations

  • D. Christodoulou
  • S. Klainerman

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