Virtual dipoles and large fluctuations in quantum gravity

TL;DR

This paper explores how large quantum fluctuations in gravitational fields can occur at various scales due to specific configurations satisfying certain conditions, challenging traditional energy constraints in quantum gravity.

Contribution

It introduces a mechanism involving localized weak field configurations with zero Einstein action, constructed via unphysical dipolar sources, and discusses modifications with cosmological or external fields.

Findings

Large quantum fluctuations can occur beyond Planck scale.

Configurations with zero Einstein action can be constructed.

Implications for stability and decay of Minkowski space.

Abstract

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 int d4x sqrt{g}R = 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.