The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to reduce the effective dimensionality, we have performed a Monte Carlo simulation of the path integral with transition probability
. Although this choice does not allow to reproduce the full dynamics, it does lead us to find a large ensemble of metric configurations having action
by several magnitude orders. These vacuum fluctuations are strong deformations of the flat space metric (for which
exactly). They exhibit a periodic polarization in the scalar curvature
R. In the simulation we fix a length scale
L and divide it into
N sub-intervals. The continuum limit is investigated by increasing
N up to
; the average squared action
is found to scale as
and thermalization of the algorithm occurs at a very low temperature (classical limit). This is in qualitative agreement with analytical results previously obtained for theories with stabilized conformal factor in the asymptotic safety scenario.
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