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Fischer, Arthur E.; Marsden, Jerrold E.; Moncrief, Vincent
The structure of the space of solutions of Einstein's equations. I. One Killing field. Annales de l'I.H.P. Physique théorique, 33 no. 2 (1980), p. 147-194
Texte intégral djvu | pdf | Analyses MR 605194 | Zbl 0454.53044

URL stable: http://www.numdam.org/item?id=AIHPA_1980__33_2_147_0

Bibliographie

R. Abraham and J. Marsden, Foundations of Mechanics, 2nd edition, Benjamin/Cummings, Reading, Massachusetts, 1978.  MR 515141 |  Zbl 0393.70001
J. Arms, Linearization stability of the Einstein-Maxwell system. J. Math. Phys., t. 18, 1977, p. 830-833.  MR 446295
J. Arms, On coupled gravitational and gauge fields. J. Math. Phys., t. 20, 1979, p. 443-453.  MR 525105
J. Arms and J. Marsden, The absence of Killing vector fields is necessary for linearization stability of Einstein's equations. Indiana Univ. Math. J., t. 28, 1979, p. 119-125.  MR 523627 |  Zbl 0405.53046
M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Diff. Geom., t. 3, 1969, p. 379-392.  MR 266084 |  Zbl 0194.53103
J. Bourgnion, D. Ebin and J. Marsden, Sur le noyau des opérateurs pseudo-différentiels a symbole surjective et non-injective. C. R. Acad. Sci., t. 282, 1976, p. 867-870.  Zbl 0323.58020
D. Brill and S. Deser, Instability of closed spaces in general relativity. Comm. Math. Phys., t. 32, 1973, p. 291-304.
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M. Buchner, J. Marsden and S. Schechter, Differential topology and singularity theory in the solution of nonlinear equations (to appear), 1979.
R. Budic, J. Isenberg, L. Lindblom and P. Yasskin, On the determination of Cauchy surfaces from intrinsic properties. Comm. Math. Phys., t. 61, 1977, p. 87-93.
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Y. Choquet-Bruhat, A. Fischer and J. Marsden, Maximal hypersurfaces and positivity of mass, in Proceedings of the International School of Physics « Enrico Fermi », Course LXVII, Isolated Gravitating Systems in General Relativity, ed. J. Ehlers, North Holland Publishing Company, Amsterdam, New York.
B. Coll, Sur la stabilité linéaire des équations d'Einstein du vide. C. R. Acad. Sci. Paris, t. 282, 1976, p. 247-250.  MR 401037 |  Zbl 0322.35055
D. Ebin, On the space of Riemannian metrics. Symp. Pure Math. Amer. Math. Soc., t. 15, 1970, p. 11-40.  MR 267604 |  Zbl 0205.53702
D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an uncompressible fluid. Ann. Math., t. 42, 1970, p. 102-163.  MR 271984 |  Zbl 0211.57401
A. Fischer and J. Marsden, Linearization stability of the Einstein equations. Bull. Am. Math. Soc., t. 79, 1973, p. 997-1003.
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A. Fischer and J. Marsden, Linearization stability of the nonlinear partial differential equations. Proc. Symp. Pure Math. A. M. S., t. 27, 1975 a, part 2, p. 219-263.  MR 383456 |  Zbl 0314.53031
A. Fischer and J. Marsden, Deformations of the scalar curvature. Duke Math. J., t. 42, 1975 b, p. 519-547.
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A. Fischer and J. Marsden, The Initial Value Problem and the Canonical Formalism of General Relativity, in Gravitational Theories since Einstein, ed. S. W. Hawking and W. Israel, Cambridge University Press, Cambridge, 1979 a.
A. Fischer and J. Marsden, Topics in the dynamics of general relativity, in Proceedings of the International School of Physics « Enrico Fermi », Course LXVII, Isolated Gravitating Systems in General Relativity, ed. J. Ehlers, North Holland Publishing Company, Amsterdam, New York, 1979 b.  MR 641404
S.W. Hawkings and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1973.  MR 424186 |  Zbl 0265.53054
R.T. Jantzen, The dynamical degrees of freedom in spatially homogeneous cosmology. Comm. Math. Phys., t. 64, 1979, p. 211-232.
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J. Marsden, Qualitative methods in bifurcation theory. Bull. Am. Math. Soc., t. 84, 1978, 1125-1148.
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J. Marsden, Geometric methods in Mathematical Physics, CBMS regional conference series, American Mathematical Society, 1980.  MR 569294 |  Zbl 0485.70001
J. Marsden and F. Tipler, Maximal hypersurfaces and foliations of constant mean curvature in general relativity (to appear), 1978.  MR 598585
C.W. Misner, R.S. Thorne and J.A. Wheeler, Gravitation, W. H. Freeman and Company, San Francisco, 1974.
V. Moncrief, Spacetime symmetries and linearization stability of the Einstein equations I. J. Math. Phys., t. 16, 1975 a, p. 493-498.  MR 363398 |  Zbl 0314.53035
V. Moncrief, Decompositions of gravitational perturbations. J. Math. Phys., t. 16, 1975 b, p. 1556-1560.  MR 371350
V. Moncrief, Spacetime symmetries and linearization stability of the Einstein equations II. J. Math. Phys., t. 17, 1976, p. 1893-1902.  MR 416469
V. Moncrief, Invariant states and quantized gravitational perturbations. Phys. Rev., t. D 18, 1978, p. 983-989.  MR 496394
R. Palais, Global formulation of Lie theory of transformation groups, in Memoris A. M. S., t. 22, 1957.  MR 121424 |  Zbl 0178.26502
R. Palais, The Morse lemma on Banach spaces. Bull. Am. Math. Soc., t. 75, 1969, p. 968-971.
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A.H. Taub, Approximate stress energy tensor for gravitational fields. J. Math. Phys., t. 2, 1961, p. 787-793.  MR 187888 |  Zbl 0112.21901
A.H. Taub, Variational principles in general relativity, ed. C. Cattanes (Lectures at the Centro Internazionale Matematico Estiud, Bressanone), Edizioni Cremonese, Rome, 1970, p. 206-300.  MR 290763
A.J. Tromba, Almost Riemannian structures on Banach manifolds, the More lemma, and the Darboux theorem. Can. J. Math., t. 28, 1976, p. 640-652.  MR 402799 |  Zbl 0345.58005
J.A. Wolf, Spaces of Constant Curvature, 3rd edition, J. A. Wolf, Berkeley, California, 1974.  MR 343214 |  Zbl 0281.53034
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