On the existence of global solutions for $T^3$-Gowdy spacetimes with stringy matter

We show a global existence theorem for Einstein-matter equations of $T^3$-Gowdy symmetric spacetimes with stringy matter. The areal time coordinate is used. It is shown that this spacetime has a crushing singularity into the past. From these results we can show that the spacetime is foliated by compact hypersurfaces of constant mean curvature.