  We generate numerically on a lattice an ensemble of stationary metrics, with
spherical symmetry, which have Einstein action $S_E \ll \hbar$. This is
obtained through a Metropolis algorithm with weight $\exp(-\beta^2 S^2_E)$ and
$\beta \gg \hbar^{-1}$. The squared action in the exponential allows to
circumvent the problem of the non-positivity of $S_E$. The discretized metrics
obtained exhibit a spontaneous polarization in regions of positive and negative
scalar curvature. We compare this ensemble with a class of continuous metrics
previously found, which satisfy the condition $S_E=0$ exactly, or in certain
cases even the stronger condition $R({\bf x})=0$ for any ${\bf x}$. All these
gravitational field configurations are of considerable interest in quantum
gravity, because they represent possible vacuum fluctuations and are markedly
different from Wheeler's "spacetime foam".
