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Linearization stability of the Einstein equations. (English) Zbl 0274.58003

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58B10 Differentiability questions for infinite-dimensional manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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[1] R. Arnowitt, S. Deser, and C. W. Misner, The dynamics of general relativity, Gravitation: An introduction to current research, Wiley, New York, 1962, pp. 227 – 265. · Zbl 0098.19103
[2] M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379 – 392. · Zbl 0194.53103
[3] Dieter R. Brill and Stanley Deser, Instability of closed spaces in general relativity, Comm. Math. Phys. 32 (1973), 291 – 304. · Zbl 0263.53042
[4] D. Brill and S. Deser, Variational methods and positive energy in relativity, Ann. Physics 50 (1968), 548-570.
[5] Yvonne Choquet-Bruhat and Stanley Deser, Stabilité initiale de l’espace temps de Minkowski, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A1019 – A1021 (French).
[6] David G. Ebin, The manifold of Riemannian metrics, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 11 – 40.
[7] Arthur Elliot Fischer, The theory of superspace, Relativity (Proc. Conf. Midwest, Cincinnati, Ohio, 1969) Plenum, New York, 1970, pp. 303 – 357.
[8] Arthur E. Fischer and Jerrold E. Marsden, The Einstein equations of evolution — a geometric approach, J. Mathematical Phys. 13 (1972), 546 – 568. · Zbl 0233.58009 · doi:10.1063/1.1666014 · doi.org
[9] Arthur E. Fischer and Jerrold E. Marsden, The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I, Comm. Math. Phys. 28 (1972), 1 – 38. · Zbl 0247.35082
[10] Arthur E. Fischer and Jerrold E. Marsden, Manifolds of Riemannian metrics with prescribed scalar curvature, Bull. Amer. Math. Soc. 80 (1974), 479 – 484. · Zbl 0288.53040
[11] Arthur E. Fischer and Jerrold E. Marsden, Linearization stability of the Einstein equations, Bull. Amer. Math. Soc. 79 (1973), 997 – 1003. · Zbl 0274.58003
[12] André Lichnerowicz, Propagateurs et commutateurs en relativité générale, Inst. Hautes Études Sci. Publ. Math. 10 (1961), 56 (French). · Zbl 0098.42607
[13] Joseph A. Wolf, Spaces of constant curvature, 2nd ed., Department of Mathematics, University of California, Berkeley, Calif., 1972. · Zbl 1216.53003
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