Traversable wormholes with electric and magnetic charges in general relativity theory

Abstract

In this work, static and spherically symmetric solutions of the general relativity coupled to linear/nonlinear electrodynamics and a dust fluid (GR-ED-DF) are studied. We demonstrate that these solutions can be categorized into two sets, both having an electromagnetically charged metric, but with the following conditions: (i) a variable redshift function, without a dust fluid as source, and (ii) a constant redshift function, with a dust fluid as source. Using (i), we provide a simple proof of the nonexistence of static and spherically symmetric traversable Morris-Thorne wormhole solutions with variable redshift functions in GR-ED-DF. Whereas using (ii), we construct several static and spherically symmetric traversable Morris-Thorne wormholes with constant redshift function in GR-ED-DF, where the source of gravity consists of a dust fluid having negative energy density and an electromagnetic field described by a physically reasonable model of linear/nonlinear electrodynamics with Lagrangian density $\mathcal{L}(\mathcal{F})$ depending only on the electromagnetic invariant $\mathcal{F}\!=\!F_{αβ}F^{αβ}\!/4$, where $F_{αβ}$ are the components of the electromagnetic field tensor. We show that in the limit of the weak electromagnetic field, each of our solutions become a traversable wormhole of the electromagnetically charged Ellis-Bronnikov wormhole type. Additionally, we present a theorem that establishes when an electrically and magnetically charged Ellis-Bronnikov wormhole, with null $\mathcal{F}$, can be supported by a GR-ED-DF theory.