3.3 Spatially inhomogeneous solutions3 Global symmetric solutions3.1 Stationary solutions

3.2 Spatially homogeneous solutions 

A solution of the Einstein equations is called spatially homogeneous if there exists a group of symmetries with three-dimensional spacelike orbits. In this case there are at least three linearly independent spacelike Killing vector fields. For most matter models the field equations reduce to ordinary differential equations. (Kinetic matter leads to an integro-differential equation.) The most important results in this area have been reviewed in a recent book edited by Wainwright and Ellis[81]. See, in particular, part two of the book. There remain a host of interesting and accessible open questions. The spatially homogeneous solutions have the advantage that it is not necessary to stop at just existence theorems; information on the global qualitative behaviour of solutions can also be obtained. An important open question concerns the mixmaster solution, as discussed in [73].

3.3 Spatially inhomogeneous solutions3 Global symmetric solutions3.1 Stationary solutions

image Local and global existence theorems for the Einstein equations
Alan D. Rendall
http://www.livingreviews.org/lrr-1998-4
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