The global existence problem in general relativity

Abstract

We survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes containing a compact Cauchy surface. We consider spacetimes with an $\ell$-dimensional Lie algebra of space-like Killing fields. For each $\ell \le 3$, we give some basic results and conjectures on global existence and cosmic censorship.

49 pages, 12 figures, based on talk given at the Arthur L. Besse Table Ronde de Géométrie Pseudo-Riemannienne Globale, Nancy, June 1998. Major revision, corresponds to published version

References in corpus (5)

• Quiescent cosmological singularities
• Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
• Curvature blow up in Bianchi VIII and IX vacuum spacetimes
• Dynamics of magnetic Bianchi VI_0 cosmologies
• Asymptotic Behavior in Polarized {\bf T}${}^2$-symmetric Vacuum Spacetimes

Cited by in corpus (3)

• Applications of the theory of evolution equations to general relativity
• Mathematical general relativity: a sampler
• Regularity of Horizons and The Area Theorem