A Global Foliation of Einstein–Euler Spacetimes with Gowdy-Symmetry on T3
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- 作者：1. Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique ; Université Pierre et Marie Curie (Paris 6) ; 4 Place Jussieu ; 75252 Paris ; France2. Max-Planck-Institut für Gravitationsphysik ; Albert-Einstein Institut ; Am Mühlenberg 1 ; 14476 Potsdam ; Germany
- 刊名：Archive for Rational Mechanics and Analysis
- 出版年：2011
- 出版时间：September 2011
- 年：2011
- 卷：201
- 期：3
- 页码：841-870
- 全文大小：304.9 KB
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- 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Mechanics
Electromagnetism, Optics and Lasers
Mathematical and Computational Physics
Complexity
Fluids - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-0673
文摘
We investigate the initial value problem for the Einstein–Euler equations of general relativity under the assumption of Gowdy symmetry on T 3, and we construct matter spacetimes with low regularity. These spacetimes admit both impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (that is, discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development, and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein–Euler equations.