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An analysis is given of particlelike nonlinear bound states in the Newtonianlimit of the coupled Einstein-Dirac system introduced by Finster, Smoller andYau. A proof is given of existence of these bound states in the almostNewtonianian regime, and it is proved that they may be approximated by theenergy minimizing solution of the Newton-Schr\"odinger system obtained by Lieb.

Existence and Newtonian limit of nonlinear bound states in the Einstein-Dirac system