  We study a novel set of gravitational field configurations, called "dipolar
zero modes", which give an exactly null contribution to the Einstein action and
are thus candidates to become large fluctuations in the quantized theory. They
are generated by static unphysical sources satisfying (up to terms of order
G^2) the simple condition Int d^3x T_00(x) = 0. We give two explicit examples
of virtual sources: (i) a "mass dipole" consisting of two separated mass
distributions with different signs; (ii) two concentric "+/- shells". The field
fluctuations can be large even at macroscopic scale. There are some, for
instance, which last ~ 1 s or more and correspond to the field generated by a
virtual source with size ~ 1 cm and mass ~ 10^6 g. This appears paradoxical,
for several reasons, both theoretical and phenomenological. We also give an
estimate of possible suppression effects following the addition to the pure
Einstein action of cosmological or R^2 terms.
