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January 2022
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GdT Thésards : N. Grubic
Einstein-Euler spacetimes with Gowdy symmetry on T^3 - Nastasia grubic
We consider the class of Gowdy-symmetric spacetimes on $T^3$ governed by the Einstein-Euler equations, where we solve the initial value problem when the initial data have solely bounded variation and the fluid variables may contain shock waves. Analyzing, both, future expanding initial data and future contracting ones, we establish the existence of a global foliation by spacetime hypersurfaces so that the time function coincides with the area of the surfaces of symmetry. Our method of proof is based on a version of the random choice scheme adapted to the Einstein
equations and the symmetry class under consideration.