1,666 research outputs found
Asymptotic Behavior of the Gowdy Spacetimes
We present new evidence in support of the Penrose's strong cosmic censorship
conjecture in the class of Gowdy spacetimes with 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
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