Consider now the Einstein equations coupled to a perfect fluid with the radiation equation of state . Then it has been shown [61, 36] that solutions with an isotropic singularity are determined uniquely by certain free data given at the singularity. The data which can be given is, roughly speaking, half as large as in the case of a regular Cauchy hypersurface. The method of proof is to derive an existence and uniqueness theorem for a suitable class of singular hyperbolic equations. Generalizations of this by Anguige and Tod have been discussed in . Details will be given in Anguige's thesis. Related work was done earlier in a somewhat simpler context by Moncrief who showed the existence of a large class of spacetimes with Cauchy horizons.
|Local and global existence theorems for the Einstein
Alan D. Rendall
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