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relativity", Exact solutions of Einstein's field equations, Learn how and when to remove these template messages, Learn how and when to remove this template message, Friedmann–Lemaître–Robertson–Walker metric, "Local and Global Existence Theorems for the Einstein Equations", https://en.wikipedia.org/w/index.php?title=Exact_solutions_in_general_relativity&oldid=960946108, Wikipedia articles needing clarification from March 2007, All Wikipedia articles needing clarification, Articles needing expert attention with no reason or talk parameter, Articles needing unspecified expert attention, Articles needing expert attention from March 2017, Articles with multiple maintenance issues, All articles with specifically marked weasel-worded phrases, Articles with specifically marked weasel-worded phrases from March 2017, Wikipedia articles needing clarification from March 2017, Creative Commons Attribution-ShareAlike License, declare the resulting symmetric second rank tensor field to be the, One can fix the form of the stress–energy tensor (from some physical reasons, say) and study the solutions of the Einstein equations with such right hand side (for example, if the stress–energy tensor is chosen to be that of the perfect fluid, a spherically symmetric solution can serve as a, null electrovacuums and null dusts have Segre type, "Time machines", i.e. This chapter is concerned with metrics admitting a group of motionstransitive on S3 or T3. These are analogous to the Bäcklund transformations known from the theory of certain partial differential equations, including some famous examples of soliton equations.

. Any Lorentzian manifold is a solution of the Einstein field equation for some right hand side. Zentralblatt MATH'This is clearly a most valuable reference book. Du kanske gillar. Einstein's General Relativity is the leading theory of space-time and gravity: it is highly nonlinear.

General Relativity and Gravitation'... a remarkable work, and indispensable to any serious practitioner of classical general relativity.'

G Studying Exact Solutions to Einstein’s Equations • In the first edition of "Exact Solutions of Einstein's Field Equations" by Kramer, Stephani, Herlt, MacCallum and Schmutzer, Cambridge University Press, 1980, the authors collected 2000 papers on exact solutions. Einstein also recognized another element of the definition of an exact solution: it should be a Lorentzian manifold (meeting additional criteria), i.e.

Any spacetime may evolve into a time machine, but it never has to do so.[5].

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