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Living Reviews in Relativity
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Local and global existence theorems for the Einstein equations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Preprint 26 Jan 1998Embargo end date: 01 Jan 2000 English Publisher:Springer Science and Business Media LLCJournal:Living Reviews in Relativity, volume 1 (issn: 2367-3613, eissn: 1433-8351, Copyright policy )
Authors: Rendall, A.;

doi: 10.12942/lrr-1998-4 , 10.12942/lrr-2000-1 , 10.48550/arxiv.gr-qc/0001008

pmid: 28191827 , 28163629

pmc: PMC5256112 , PMC5253797

arXiv: gr-qc/0001008

handle: 11858/00-001M-0000-0013-5799-D , 11858/00-001M-0000-0013-5798-F

Local and global existence theorems for the Einstein equations

Abstract

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.

35 pages. To appear in Living Reviews in Relativity

Related Organizations
Keywords

Cauchy problem, Special relativity, Physics and Astronomy (miscellaneous), special relativity, Newtonian theory, FOS: Physical sciences, Exact solutions to problems in general relativity and gravitational theory, Review Article, General Relativity and Quantum Cosmology (gr-qc), Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory, General Relativity and Quantum Cosmology, singularity structure, Einstein's equations (general structure, canonical formalism, Cauchy problems), Atomic physics. Constitution and properties of matter, Einstein equation, existence theorem, Space-time singularities, cosmic censorship, etc., QC170-197

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
29
Average
Top 10%
Top 10%
Green
gold