eng
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Living Reviews in Relativity
1433-8351
2000-01-07
3
1
10.12942/lrr-2000-1
lrr-2000-1
article
Local and Global Existence Theorems for the Einstein Equations
Alan D. Rendall
1
Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14424 Golm, Germany
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.
http://www.livingreviews.org/lrr-2000-1