General Relativity and Quantum Cosmology, abstract

On ``asymptotically flat" space--times with $G_{2}$--invariant Cauchy surfaces

Authors: B.Berger, P.T. Chrusciel, V.Moncrief
Comments: 33 pages, Latex (with amssymbols), Garching preprint MPA 797
Journal-ref: Annals Phys. 237 (1995) 322-354

In this paper we study space-times which evolve out of Cauchy data $(\Sigma,\metrict,K)$ invariant under the action of a two-dimensional commutative Lie group. Moreover $(\Sigma,\metrict,K)$ 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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