Can Reissner-Nordstr\"{o}m wormholes be considered for Spacetime Foam formation?

Abstract

A simple model of spacetime foam, made by $N$ Reissner-Nordstr\"{o}m wormholes with a magnetic and electric charge in a semiclassical approximation, is taken under examination. The Casimir-like energy of the quantum fluctuation of such a model is computed and compared with that one obtained with a foamy space modeled by $N$ Schwarzschild wormholes. The comparison leads to the conclusion that a foamy spacetime cannot be considered as a collection of $N$ Reissner-Nordstr\"{o}m wormholes but that such a collection can be taken as an excited state of the foam.