On properties of the distribution of virtual wormholes in a vacuum

Abstract

A model of space-time foam in the form of an arbitrary distribution of spherical Euclidean wormholes is considered. A method for constructing the exact solution of Einstein's Euclidean equations for the metric corresponding to this model is proposed. In the framework of our model we obtain the expression for the Euclidean action and its dependence on the parameters of wormholes in the explicit form. It is shown how the solutions obtained make it possible to determine all possible correlation functions associated with the parameters of virtual wormholes in the vacuum state.