On "Asymptotically Flat" Space-Times with G2-Invariant Cauchy Surfaces

In this paper we study space-times which evolve out of Cauchy data (Σ, 3g, K) invariant under the action of a two-dimensional commutative Lie group. Moreover, (Σ 3g, 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 R3, 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.