Charged traversable wormholes: charge without charge

TL;DR

This work constructs a charged traversable wormhole in the Einstein–Maxwell framework supported by anisotropic matter, deriving explicit static solutions with $f(r)$, $g(r)$, throat relations, and a Maxwell field that embodies the charge without net flux, while examining flare-out, exoticity, and tidal constraints. It further tackles the challenge of rotating wormholes by applying a modified Newman–Janis procedure to obtain a rotating geometry with new metric functions $F$ and $G$, and analyzes the resulting geometric and observational features, noting unresolved issues such as the vanishing of $G_{r\theta}$ and the Maxwell sector for rotation. The study demonstrates that charge can influence throat size and tidal forces, and that photon-sphere and light-deflection signatures can arise in wormhole spacetimes, offering potential observational discriminants from black holes. Overall, it provides a concrete realization of the charge-without-charge concept and establishes a groundwork for rotating charged wormholes, while outlining key theoretical hurdles and directions for future work.

Abstract

We present and investigate charged wormhole solutions of the Einstein-Maxwell equations supported by anisotropic matter fields, with the purpose of establishing their physical plausibility as traversable wormholes. To this end, we examine the flare-out condition and evaluate tidal forces to confirm their traversability. We also analyze light deflection around these wormholes to provide observational implications. Additionally, we attempt to construct rotating generalizations of the solutions by applying and modifying the Newman-Janis algorithm. Our results suggest that the obtained geometries offer a concrete realization of the concept of ``charge without charge".

Figures (6)

• Figure 1: (color online). Conceptual embedded diagram of the wormhole with electric field lines.
• Figure 2: (color online). The magnitude of tidal accelerations at the throat. The $v_d$, $r_d$, and $Q_d$ are introduced to make dimensionless quantities with the unit quantity.
• Figure 3: (color online) The effective potential
• Figure 4: (color online) The capture cross-section of light by a wormhole.
• Figure 5: (color online) The deflection angle by a wormhole.