  The coupled Einstein-Dirac equations for a static, spherically symmetric
system of two fermions in a singlet spinor state are derived. Using numerical
methods, we construct an infinite number of soliton-like solutions of these
equations. The stability of the solutions is analyzed. For weak coupling (i.e.,
small rest mass of the fermions), all the solutions are linearly stable (with
respect to spherically symmetric perturbations), whereas for stronger coupling,
both stable and unstable solutions exist. For the physical interpretation, we
discuss how the energy of the fermions and the (ADM) mass behave as functions
of the rest mass of the fermions. Although gravitation is not renormalizable,
our solutions of the Einstein-Dirac equations are regular and well-behaved even
for strong coupling.
