Abstract
In this paper we study space-times which evolve out of Cauchy data (Σ, 3 g, K) invariant under the action of a two-dimensional commutative Lie group. Moreover, (Σ 3 g, K) are assumed to satisfy certain completeness and asymptotic flatness conditions in spacelike directions. We show that asymptotic flatness and energy conditions exclude all topologies and group actions except for a cylindrically symmetric R 3, or a periodic identification thereof along the z-axis. We prove that asymptotic flatness, energy conditions, and cylindrical symmetry exclude the existence of compact trapped surfaces. Finally, we show that the recent results of Christodoulou and Tahvildar-Zadeh concerning global existence of a class of wave-maps imply that strong cosmic censorship holds in the class of asymptotically flat cylindrically symmetric electro-vacuum space-times.
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