Class of Einstein-Maxwell Phantom Fields: Rotating and Magnetised Wormholes

TL;DR

This paper develops a method to find exact axially symmetric solutions in general relativity with phantom scalar fields, revealing new rotating wormhole solutions with magnetic monopoles and dipoles.

Contribution

Introduces a new ansatz for solving Einstein equations with phantom scalar fields, enabling derivation of simple, exact rotating wormhole solutions with magnetic and gravitational multipoles.

Findings

Derived exact rotating wormhole solutions with magnetic monopoles and dipoles.

Established a systematic procedure for solving Einstein-phantom scalar field equations.

Presented solutions that include gravitational multipole fields.

Abstract

Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general relativity. We focus on the solutions which represent wormholes. The procedure presented in this work allows to derive new exact solutions up to very simple integrations. Among other results, I find exact rotating solutions containing magnetic monopoles, dipoles, etc., coupled to Phantom scalar and to gravitational multipole fields.