Traversable wormholes with electric and magnetic charges in general relativity theory

TL;DR

This paper explores static, spherically symmetric traversable wormholes in general relativity coupled with electrodynamics and dust, proving their nonexistence with variable redshift functions and constructing solutions with constant redshift functions supported by exotic matter.

Contribution

It provides a classification of solutions, proves the nonexistence of certain wormholes, and constructs new traversable wormhole solutions supported by negative energy density dust and electromagnetic fields.

Findings

Proves no static, spherically symmetric traversable wormholes with variable redshift functions exist in GR-ED-DF.

Constructs explicit traversable wormhole solutions with constant redshift functions supported by exotic matter.

Shows solutions reduce to Ellis-Bronnikov wormholes in weak electromagnetic field limit.

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 $\mathcal{F}\!=\!F_{\alpha\beta}F^{\alpha\beta}\!/4$, where $F_{\alpha\beta}$ 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.