Comptes Rendus
no. 2
Mathematical Physics
Future complete S1 symmetric Einsteinian spacetimes, the unpolarized case
[Espaces temps einsteinians complets vers le futur]

Présenté par : Yvonne Choquet-Bruhat

Yvonne Choquet-Bruhat1
1 Université Paris 6, LPTL, 4, place Jussieu, 75232 Paris, France
Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 129-136.

On démontre l'existence d'espaces temps génériques, à symétrie S1 mais non polarisés, complets dans la direction de l'expansion, pour des données initiales petites.

We prove the existence of vacuum S1 symmetric Einsteinian, unpolarized, space times which are complete in the direction of the expansion, for small initial data.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00277-2
Yvonne Choquet-Bruhat 1

1 Université Paris 6, LPTL, 4, place Jussieu, 75232 Paris, France 
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Yvonne Choquet-Bruhat. Future complete S1 symmetric Einsteinian spacetimes, the unpolarized case. Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 129-136. doi : 10.1016/S1631-073X(03)00277-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00277-2/

[1] L. Andersson; V. Moncrief; A. Tromba On the global evolution problem in 2+1 gravity, J. Geom. Phys., Volume 23 (1997) no. 3–4, pp. 1991-2205

[2] Y. Choquet-Bruhat Global wave maps on curved spacetimes (Cotsakis; Gibbons, eds.), Mathematical and Quantum Aspects of Relativity and Cosmology, Lecture Notes in Phys., 535, Springer, 1998, pp. 1-30

[3] Y. Choquet-Bruhat Wave maps in general relativity (A. Harvey, ed.), On Einstein Path, Springer, 1998, pp. 161-185

[4] Y. Choquet-Bruhat; S. Cotsakis Global hyperbolicity and completeness, J. Geom. Phys., Volume 43 (2002) no. 4, pp. 345-350

[5] Y. Choquet-Bruhat, C. DeWitt–Morette, Analysis Manifolds and Physics II, pp. 478–483

[6] Y. Choquet-Bruhat; V. Moncrief Existence theorem for solutions of Einstein equations with 1 parameter spacelike isometry group (H. Brezis; I.E. Segal, eds.), Proc. Sympos. Pure Math., 59, 1996, pp. 67-80

[7] Y. Choquet-Bruhat; V. Moncrief Future global in time Einsteinian spacetimes with U(1) isometry group, Ann. Inst. H. Poincaré, Volume 2 (2001), pp. 1007-1064

[8] Y. Choquet-Bruhat, V. Moncrief, Nonlinear stability of Einsteinian spacetimes with U(1) isometry group, in: Kajitani, Vaillant (Eds.), Partial Differential Equations and Mathematical Physics, in honor of J. Leray, Birkhäuser, to appear

[9] A. Fisher; A. Tromba Teichmuller spaces, Math. Ann., Volume 267 (1984), pp. 311-345

[10] V. Moncrief Reduction of Einstein equations with spacelike U(1) isometry group, Ann. of Phys., Volume 167 (1986), pp. 118-142

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