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

TL;DR

This paper investigates asymptotically flat space-times with G2 symmetry, demonstrating that under certain conditions, only cylindrical topologies are possible and that strong cosmic censorship holds in this class.

Contribution

It characterizes the topology and symmetry constraints of asymptotically flat space-times with G2 invariance and proves strong cosmic censorship for this class.

Findings

Excludes all topologies except cylindrical symmetry under given conditions.

Shows absence of compact trapped surfaces in these space-times.

Establishes strong cosmic censorship for asymptotically flat cylindrically symmetric electro-vacuum space-times.

Abstract

In this paper we study space-times which evolve out of Cauchy data $(\Sigma,{}^3g,K)$ invariant under the action of a two-dimensional commutative Lie group. Moreover $(\Sigma,{}^3g,K)$ 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 $R^3$, 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.