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In 1916 Einstein published his famous paper "The foundation of the general theory of relativity". It changed our view of the universe forever. Unfortunately, the mathematical content of his general theory reduces to a set of ten highly nonlinear, coupled, hyperbolic and elliptic partial differential equations that are among the most complicated in mathematical physics. They cannot easily be studied analytically, except in a handful of idealized cases involving specialized symmetries or approximations.
Anninos et al. (Mon,) studied this question.