The singular equations which arise in the study of isotropic
singularities are closely related to what Kichenassamy [105] calls Fuchsian equations. He has developed a rather general
theory of these equations. (See [105], [104], [103], and also the earlier papers [12], [106] and [107].) In [108] this was applied to analytic Gowdy spacetimes to construct a
family of vacuum spacetimes depending on the maximum number of
free functions (for the given symmetry class) whose singularities
can be described in detail. The symmetry assumed in that paper
requires the twosurfaces orthogonal to the group orbits to be
surfaceforming (vanishing twist constants). In [97] a corresponding result was obtained for the class of vacuum
spacetimes with polarized
symmetry and nonvanishing twist.
A result of Anguige [6] is of a similar type but there are several significant
differences. He considers perfect fluid spacetimes and can handle
smooth data rather than only the analytic case. On the other hand
he assumes plane symmetry, which is stronger than Gowdy
symmetry.
Related work was done earlier in a somewhat simpler context by
Moncrief [121] who showed the existence of a large class of analytic vacuum
spacetimes with Cauchy horizons.

Local and Global Existence Theorems for the Einstein
Equations
Alan D. Rendall
http://www.livingreviews.org/lrr20001
© MaxPlanckGesellschaft. ISSN 14338351
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