For Einstein's equations, there appear to be subtle differences compared with other fields : they are self-interacting ( that is, non-linear even in the absence of other fields ); they are diffeomorphism invariant, so to obtain a unique solution, a fixed background metric and gauge conditions need to be introduced; finally, the metric determines the spacetime structure, and thus the domain of dependence for any set of initial data, so the region on which a specific solution will be defined is not, a priori, defined.
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