Phantom wormholes in Einstein-Maxwell-dilaton theory

TL;DR

This paper presents a new electrically charged traversable wormhole solution in Einstein-Maxwell-dilaton theory with a phantom dilaton, exploring its properties, dualities, and light deflection characteristics.

Contribution

The paper introduces a novel wormhole solution with a phantom dilaton in Einstein-Maxwell-dilaton theory, analyzing its topological scalar field, duality transformations, and gravitational lensing effects.

Findings

Recovered anti-Fisher and Bronnikov-Ellis solutions in special limits

Computed the topological charge of the scalar field

Determined the wormhole throat position and light deflection angle

Abstract

In this paper we give an electrically charged traversable wormhole solution for the Einstein-Maxwell-dilaton theory when the dilaton is a phantom field, i.e. it has flipped sign kinetic term appearing in the action. In the limit when the charge is zero, we recover the anti-Fisher solution, which can be reduced to the Bronnikov-Ellis solution under certain choices of integration constants. The equations of motion of this theory share the same S-duality invariance of string theory, so the electrically charged solution is rotated into the magnetically charged one by applying such transformations. The scalar field is topological, so we compute its topological charge, and discuss that under appropriate boundary conditions we can have a lump, a kink, or an anti-kink profile. We determine the position of the throat, and show the embedding diagram of the wormhole. As a physical application, we apply the Gauss-Bonnet theorem to compute the deflection angle of a light-ray that passes close to the wormhole.