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

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

1994-04-06

arxiv.org/abs/gr-qc/9404005v1

Ann.Phys.237:322-354,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, Latex (with amssymbols), Garching preprint MPA 797

Scientific paper

10.1006/aphy.1995.1012

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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