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Analytic description of singularities in Gowdy spacetimes
Satyanad Kichenassamy and Alan D. Rendall
We use the Fuchsian algorithm to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other known solutions. The method provides precise asymptotics at the singularity, which is Kasner-like. All of these solutions are asymptotically velocity-dominated. The results account for the fact that solutions with velocity parameter uniformly greater than one are not observed numerically. They also provide a justification of formal expansions proposed by Grubisic and Moncrief.