# General Relativity and Quantum
Cosmology, abstract

gr-qc/9404005

## 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.