@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},
year = {1980},
publisher = {Gauthier-Villars},
volume = {33},
number = {2},
mrnumber = {605194},
zbl = {0454.53044},
language = {en},
url = {https://www.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 - https://www.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 https://www.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. https://www.numdam.org/item/AIHPA_1980__33_2_147_0/
and , Foundations of Mechanics, 2nd edition, Benjamin/Cummings, Reading, Massachusetts, 1978. | Zbl | MR
, Linearization stability of the Einstein-Maxwell system. J. Math. Phys., t. 18, 1977, p. 830-833. | MR
, On coupled gravitational and gauge fields. J. Math. Phys., t. 20, 1979, p. 443-453. | MR
and , 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. | Zbl | MR
and , Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Diff. Geom., t. 3, 1969, p. 379-392. | Zbl | MR
, and , Sur le noyau des opérateurs pseudo-différentiels a symbole surjective et non-injective. C. R. Acad. Sci., t. 282, 1976, p. 867-870. | Zbl
and , Instability of closed spaces in general relativity. Comm. Math. Phys., t. 32, 1973, p. 291-304. | Zbl | MR
, and , Differential topology and singularity theory in the solution of nonlinear equations (to appear), 1979.
, , and , On the determination of Cauchy surfaces from intrinsic properties. Comm. Math. Phys., t. 61, 1977, p. 87-93. | Zbl | MR
, and , 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.
, Sur la stabilité linéaire des équations d'Einstein du vide. C. R. Acad. Sci. Paris, t. 282, 1976, p. 247-250. | Zbl | MR
, On the space of Riemannian metrics. Symp. Pure Math. Amer. Math. Soc., t. 15, 1970, p. 11-40. | Zbl | MR
and , Groups of diffeomorphisms and the motion of an uncompressible fluid. Ann. Math., t. 42, 1970, p. 102-163. | Zbl | MR
and , Linearization stability of the Einstein equations. Bull. Am. Math. Soc., t. 79, 1973, p. 997-1003. | Zbl | MR
and , Linearization stability of the nonlinear partial differential equations. Proc. Symp. Pure Math. A. M. S., t. 27, 1975 a, part 2, p. 219-263. | Zbl | MR
and , Deformations of the scalar curvature. Duke Math. J., t. 42, 1975 b, p. 519-547. | Zbl | MR
and , 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.
and , 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
and , The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1973. | Zbl | MR
, The dynamical degrees of freedom in spatially homogeneous cosmology. Comm. Math. Phys., t. 64, 1979, p. 211-232. | Zbl | MR
, Qualitative methods in bifurcation theory. Bull. Am. Math. Soc., t. 84, 1978, 1125-1148. | Zbl | MR
, Geometric methods in Mathematical Physics, CBMS regional conference series, American Mathematical Society, 1980. | Zbl | MR
and , Maximal hypersurfaces and foliations of constant mean curvature in general relativity (to appear), 1978. | MR
, and , Gravitation, W. H. Freeman and Company, San Francisco, 1974.
, Spacetime symmetries and linearization stability of the Einstein equations I. J. Math. Phys., t. 16, 1975 a, p. 493-498. | Zbl | MR
, Decompositions of gravitational perturbations. J. Math. Phys., t. 16, 1975 b, p. 1556-1560. | MR
, Spacetime symmetries and linearization stability of the Einstein equations II. J. Math. Phys., t. 17, 1976, p. 1893-1902. | MR
, Invariant states and quantized gravitational perturbations. Phys. Rev., t. D 18, 1978, p. 983-989. | MR
, Global formulation of Lie theory of transformation groups, in Memoris A. M. S., t. 22, 1957. | Zbl | MR
, The Morse lemma on Banach spaces. Bull. Am. Math. Soc., t. 75, 1969, p. 968-971. | Zbl | MR
, Approximate stress energy tensor for gravitational fields. J. Math. Phys., t. 2, 1961, p. 787-793. | Zbl | MR
, Variational principles in general relativity, ed. C. Cattanes (Lectures at the Centro Internazionale Matematico Estiud, Bressanone), Edizioni Cremonese, Rome, 1970, p. 206-300. | MR
, Almost Riemannian structures on Banach manifolds, the More lemma, and the Darboux theorem. Can. J. Math., t. 28, 1976, p. 640-652. | Zbl | MR
, Spaces of Constant Curvature, 3rd edition, J. A. Wolf, Berkeley, California, 1974. | Zbl | MR
