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 [79]. Details will be given in Anguige's thesis. Related work was
done earlier in a somewhat simpler context by Moncrief[59] who showed the existence of a large class of spacetimes with
Cauchy horizons.
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Local and global existence theorems for the Einstein
equations
Alan D. Rendall http://www.livingreviews.org/lrr-1998-4 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |