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Global geometry of -symmetric spacetimes with weak regularity
- Source :
-
Comptes Rendus. Mathématique . Nov2010, Vol. 348 Issue 21/22, p1231-1233. 3p. - Publication Year :
- 2010
-
Abstract
- Abstract: We define the class of weakly regular spacetimes with -symmetry, and investigate their global geometrical structure. We formulate the initial value problem for the Einstein vacuum equations with weak regularity, and establish the existence of a global foliation by the level sets of the area R of the orbits of symmetry, so that each leaf can be regarded as an initial hypersurface. Except for the flat Kasner spacetimes which are known explicitly, R takes all positive values. Our weak regularity assumptions only require that the gradient of R is continuous while the metric coefficients belong to the Sobolev space (or have even less regularity). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 348
- Issue :
- 21/22
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 55212189
- Full Text :
- https://doi.org/10.1016/j.crma.2010.09.009