Virtual dipoles and large fluctuations in quantum gravity

The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise—not only at the Planck scale, but also at larger scales. This is because there exists a set of localised weak field configurations which satisfy the condition ∫ dx √ gR = 0 and thus give a null contribution to the Einstein action. Such configurations can be constructed by solving Einstein field equations with unphysical dipolar sources. We discuss this mechanism and its modification in the presence of a cosmological term and/or an external field. 04.20.-q Classical general relativity. 04.60.-m Quantum gravity.