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

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.

24 pages

References in corpus (3)

• Strong cosmic censorship for T^2-symmetric spacetimes with cosmological constant and matter
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter

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