The structure of the space of solutions of Einstein's equations. I. One Killing field
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 33 (1980) no. 2, pp. 147-194.
@article{AIHPA_1980__33_2_147_0,
     author = {Fischer, Arthur E. and Marsden, Jerrold E. and Moncrief, Vincent},
     title = {The structure of the space of solutions of {Einstein's} equations. {I.} {One} {Killing} field},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {147--194},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {2},
     year = {1980},
     mrnumber = {605194},
     zbl = {0454.53044},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1980__33_2_147_0/}
}
TY  - JOUR
AU  - Fischer, Arthur E.
AU  - Marsden, Jerrold E.
AU  - Moncrief, Vincent
TI  - The structure of the space of solutions of Einstein's equations. I. One Killing field
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1980
SP  - 147
EP  - 194
VL  - 33
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1980__33_2_147_0/
LA  - en
ID  - AIHPA_1980__33_2_147_0
ER  - 
%0 Journal Article
%A Fischer, Arthur E.
%A Marsden, Jerrold E.
%A Moncrief, Vincent
%T The structure of the space of solutions of Einstein's equations. I. One Killing field
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1980
%P 147-194
%V 33
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1980__33_2_147_0/
%G en
%F AIHPA_1980__33_2_147_0
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'institut Henri Poincaré. Section A, Physique Théorique, Tome 33 (1980) no. 2, pp. 147-194. http://archive.numdam.org/item/AIHPA_1980__33_2_147_0/

R. Abraham and J. Marsden, Foundations of Mechanics, 2nd edition, Benjamin/Cummings, Reading, Massachusetts, 1978. | MR | Zbl

J. Arms, Linearization stability of the Einstein-Maxwell system. J. Math. Phys., t. 18, 1977, p. 830-833. | MR

J. Arms, On coupled gravitational and gauge fields. J. Math. Phys., t. 20, 1979, p. 443-453. | MR

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 | Zbl

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 | Zbl

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

D. Brill and S. Deser, Instability of closed spaces in general relativity. Comm. Math. Phys., t. 32, 1973, p. 291-304. | MR | Zbl

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. | MR | Zbl

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 | Zbl

D. Ebin, On the space of Riemannian metrics. Symp. Pure Math. Amer. Math. Soc., t. 15, 1970, p. 11-40. | MR | Zbl

D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an uncompressible fluid. Ann. Math., t. 42, 1970, p. 102-163. | MR | Zbl

A. Fischer and J. Marsden, Linearization stability of the Einstein equations. Bull. Am. Math. Soc., t. 79, 1973, p. 997-1003. | MR | Zbl

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 | Zbl

A. Fischer and J. Marsden, Deformations of the scalar curvature. Duke Math. J., t. 42, 1975 b, p. 519-547. | MR | Zbl

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

S.W. Hawkings and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1973. | MR | Zbl

R.T. Jantzen, The dynamical degrees of freedom in spatially homogeneous cosmology. Comm. Math. Phys., t. 64, 1979, p. 211-232. | MR | Zbl

J. Marsden, Qualitative methods in bifurcation theory. Bull. Am. Math. Soc., t. 84, 1978, 1125-1148. | MR | Zbl

J. Marsden, Geometric methods in Mathematical Physics, CBMS regional conference series, American Mathematical Society, 1980. | MR | Zbl

J. Marsden and F. Tipler, Maximal hypersurfaces and foliations of constant mean curvature in general relativity (to appear), 1978. | MR

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 | Zbl

V. Moncrief, Decompositions of gravitational perturbations. J. Math. Phys., t. 16, 1975 b, p. 1556-1560. | MR

V. Moncrief, Spacetime symmetries and linearization stability of the Einstein equations II. J. Math. Phys., t. 17, 1976, p. 1893-1902. | MR

V. Moncrief, Invariant states and quantized gravitational perturbations. Phys. Rev., t. D 18, 1978, p. 983-989. | MR

R. Palais, Global formulation of Lie theory of transformation groups, in Memoris A. M. S., t. 22, 1957. | MR | Zbl

R. Palais, The Morse lemma on Banach spaces. Bull. Am. Math. Soc., t. 75, 1969, p. 968-971. | MR | Zbl

A.H. Taub, Approximate stress energy tensor for gravitational fields. J. Math. Phys., t. 2, 1961, p. 787-793. | MR | Zbl

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

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 | Zbl

J.A. Wolf, Spaces of Constant Curvature, 3rd edition, J. A. Wolf, Berkeley, California, 1974. | MR | Zbl