  The aim of this Note is to prove by a perturbation method the existence of
solutions of the coupled Einstein-Dirac-Maxwell equations for a static,
spherically symmetric system of two fermions in a singlet spinor state and with
the electromagnetic coupling constant $(\frac{e}{m})^2<1$. We show that the
nondegenerate solution of Choquard's equation generates a branch of solutions
of the Einstein-Dirac-Maxwell equations.
