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In the functional integral approach to quantum gravity, the quantumconfigurations are usually treated to order hbar through a stationary phaseapproximation around the saddle point of the action where spacetime is flat. Weshow that from this point a "level line" in functional space departs, whichcomprises a family of static non-flat metrics with zero scalar curvature,depending on a continuous mass parameter. Furthermore, each of these metricscan be perturbed by an arbitrary function in such a way to still satisfy thecondition Int(gR)d4x=0. We thus find a set of zero-modes of the gravitationalaction which has non-vanishing measure in the functional space. These metricswill contribute to the functional integral as vacuum fluctuations, on the samefooting as those near the saddle point.Comment: 13 pages, 4 figures; to appear in Class. Q. Gravit

The vacuum state of quantum gravity contains large virtual masses