Future complete <i>S</i><sup>1</sup> symmetric Einsteinian spacetimes, the unpolarized case

Yvonne Choquet-Bruhat

doi:10.1016/S1631-073X(03)00277-2

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-Bruhat ¹

¹ Université Paris 6, LPTL, 4, place Jussieu, 75232 Paris, France

Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 129-136.

Résumé
Abstract

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 : 2003-05-27
Accepté le : 2003-05-27
Publié le : 2003-07-08

DOI : 10.1016/S1631-073X(03)00277-2

Affiliations des auteurs :

Yvonne Choquet-Bruhat ¹

¹ Université Paris 6, LPTL, 4, place Jussieu, 75232 Paris, France

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     author = {Yvonne Choquet-Bruhat},
     title = {Future complete {\protect\emph{S}\protect\textsuperscript{1}} symmetric {Einsteinian} spacetimes, the unpolarized case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {129--136},
     publisher = {Elsevier},
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     number = {2},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00277-2},
     language = {en},
}

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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/

Bibliographie
Cité par

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[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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