Local and global existence theorems for the Einstein equations

Details Local and global existence theorems for the Einstein equations Local and global existence theorems for the Einstein equations

2000-01-05

arxiv.org/abs/gr-qc/0001008v1

LivingRev.Rel.3:1,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages. To appear in Living Reviews in Relativity

Scientific paper

This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutions with symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. This is followed by a survey of global results in the case of small data and results on constructing spacetimes with given singularity structure. The article ends with some miscellaneous topics connected with the main theme.

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