7 Further results6 Prescribed singularities6.1 Isotropic singularities

6.2 Fuchsian equations

  The singular equations which arise in the study of isotropic singularities are closely related to what Kichenassamy [105Jump To The Next Citation Point In The Article] 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 two-surfaces orthogonal to the group orbits to be surface-forming (vanishing twist constants). In [97] a corresponding result was obtained for the class of vacuum spacetimes with polarized tex2html_wrap_inline1384 symmetry and non-vanishing 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.

7 Further results6 Prescribed singularities6.1 Isotropic singularities

image Local and Global Existence Theorems for the Einstein Equations
Alan D. Rendall
© Max-Planck-Gesellschaft. ISSN 1433-8351
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