3.5 Spatially compact solutions3 Global Symmetric Solutions3.3 Spherically symmetric solutions

3.4 Cylindrically symmetric solutions 

Solutions of the Einstein equations with cylindrical symmetry that are asymptotically flat in all directions allowed by the symmetry represent an interesting variation on asymptotic flatness. Since black holes are apparently incompatible with this symmetry, one may hope to prove geodesic completeness of solutions under appropriate assumptions. (It would be interesting to have a theorem making the statement about black holes precise.) A proof of geodesic completeness has been achieved for the Einstein vacuum equations and for the source-free Einstein-Maxwell equations in [34], building on global existence theorems for wave maps [83, 82]. For a quite different point of view on this question involving integrable systems see [243]. A recent paper of Hauser and Ernst [128] also appears to be related to this question. However, due to the great length of this text and its reliance on many concepts unfamiliar to this author, no further useful comments on the subject can be made here.

3.5 Spatially compact solutions3 Global Symmetric Solutions3.3 Spherically symmetric solutions

image Theorems on Existence and Global Dynamics for the Einstein Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2002-6
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