  The aim of this work is to prove by a perturbation method the existence of
solutions of the coupled Einstein-Dirac equations for a static, spherically
symmetric system of two fermions in a singlet spinor state. We relate the
solutions of our equations to those of the nonlinear Choquard equation and we
show that the nondegenerate solution of Choquard's equation generates solutions
for Einstein-Dirac equations.
