Asymptotic Behavior of the T3×RT^3 \times R Gowdy Spacetimes

We present new evidence in support of the Penrose's strong cosmic censorship conjecture in the class of Gowdy spacetimes with $T^3$ spatial topology. Solving Einstein's equations perturbatively to all orders we show that asymptotically close to the boundary of the maximal Cauchy development the dominant term in the expansion gives rise to curvature singularity for almost all initial data. The dominant term, which we call the ``geodesic loop solution'', is a solution of the Einstein's equations with all space derivatives dropped. We also describe the extent to which our perturbative results can be rigorously justified.Comment: 30 page

On the global evolution problem in 2+1 gravity

Existence of global CMC foliations of constant curvature 3-dimensional maximal globally hyperbolic Lorentzian manifolds, containing a constant mean curvature hypersurface with \genus(\Sigma) > 1 is proved. Constant curvature 3-dimensional Lorentzian manifolds can be viewed as solutions to the 2+1 vacuum Einstein equations with a cosmological constant. The proof is based on the reduction of the corresponding Hamiltonian system in constant mean curvature gauge to a time dependent Hamiltonian system on the cotangent bundle of Teichm\"uller space. Estimates of the Dirichlet energy of the induced metric play an essential role in the proof.Comment: 14 pages, amsar