Einstein-Euler equations for matter spacetimes with Gowdy symmetry
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2008-2009), Exposé no. 23, 15 p.

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on ${T}^{3}$. Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive gravitational waves and shock waves. The cosmic censorhip conjecture is established in the polarized case.

@article{SEDP_2008-2009____A23_0,
author = {LeFloch, Philippe G.},
title = {Einstein-Euler equations for matter spacetimes with {Gowdy} symmetry},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:23},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2008-2009},
language = {en},
url = {http://www.numdam.org/item/SEDP_2008-2009____A23_0/}
}
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LeFloch, Philippe G. Einstein-Euler equations for matter spacetimes with Gowdy symmetry. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2008-2009), Exposé no. 23, 15 p. http://www.numdam.org/item/SEDP_2008-2009____A23_0/

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