Asymptotic behavior in polarized $\mathbb T^2$-symmetric spacetimes
Résumé
We use Fuchsian Reduction to study the behavior near the
singularity of a class of solutions of Einstein’s vacuum
equations. These solutions admit two commuting spacelike Killing
fields like the Gowdy space–times, but their twist does not
vanish. The space–times are also polarized in the sense that one
of the ``gravitational degrees of freedom'' is turned off.
Examining an analytic family of solutions with the maximum number
of arbitrary functions, we find that they are all AVTD (``asymptotically
velocity-term dominated'') as one approaches the singularity.