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A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3

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Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1004.0427
(Preprint), 264KB

ARMA201_841.pdf
(Any fulltext), 305KB

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Citation

LeFloch, P. G., & Rendall, A. D. (2011). A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3. Archive for Rational Mechanics and Analysis, 201(3), 841-870. Retrieved from http://arxiv.org/abs/1004.0427.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-45EA-3
Abstract
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, 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 (i.e., 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.