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

TL;DR

This paper examines whether Reissner-Nordström wormholes can form a spacetime foam by comparing their quantum Casimir energy to that of Schwarzschild wormholes, concluding they are more likely excited states rather than fundamental components.

Contribution

It introduces a semiclassical model of spacetime foam using Reissner-Nordström wormholes and compares its quantum energy to Schwarzschild wormholes, revealing their different roles.

Findings

Reissner-Nordström wormholes are not suitable as fundamental spacetime foam constituents.

Such wormholes can be viewed as excited states within the foam.

The Casimir-like energy comparison informs the foam's structure.

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.