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Rendall, Alan D.

Theorems on existence and global dynamics for the Einstein equations. (English) Zbl 1316.83008

Living Rev. Relativ. 8, Article No. 2005-6, 68 p. (2005).
Summary: This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.
Update to author’s paper [Zbl 1316.83007], see also the updates [Zbl 0944.83002; Zbl 1024.83009]:
1. All sections have been updated and new references added with the result that the total number of references has increased by 40 per cent in comparison with the previous version
2. Section 3.4 (weak null singularities and Price’s law) is new
3. Section 3.6 (spatially compact solutions) includes a new discussion of Gowdy spacetimes
4. Section 6.3 (asymptotics for a phase of accelerated expansion) is new
5. The old section 7.3 has been much expanded to constitute the new sections 7.3-7.6.
6. Section 8.4 (cosmic censorship in Gowdy spacetimes) is new.
7. Section 9.6 (the geodesic hypothesis) is new

Cited in 18 Documents

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83A05 Special relativity
83C75 Space-time singularities, cosmic censorship, etc.

Citations:

Zbl 1316.83007; Zbl 0944.83002; Zbl 1024.83009
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References:

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