Charged multi-sheet wormhole solutions

TL;DR

This paper constructs and analyzes charged multi-sheet wormhole solutions in Einstein-Maxwell-massless phantom scalar theory, revealing broader parameter regions for regular solutions and introducing a new coordinate system for simplified expression.

Contribution

It introduces a method to generate charged wormhole solutions with multiple sheets using Harrison transformation and extends the parameter space for regular solutions.

Findings

Regular solutions exist beyond the Harrison transformation's initial parameter bounds.

A new spheroidal coordinate system simplifies the wormhole solutions.

The solutions are characterized by five parameters including mass, charges, and number of sheets.

Abstract

We construct charged wormhole solutions with an even number of asymptotically flat regions in the four-dimensional Einstein-Maxwell-massless phantom scalar system via the Harrison transformation. The solutions are characterized by five parameters: the mass $M$, the electric charge $Q_\mathrm{e}$, the magnetic charge $Q_\mathrm{m}$, the scalar charge $P$ and the number of sheets $2n$. The regularity condition then determines the throat radius. Although the Harrison transformation directly generates the solutions only in the parameter region $Q_{\mathrm{e}}^2 + Q_{\mathrm{m}}^2 < M^2$, we show that regular solutions exist in a wider parameter region beyond this bound. In addition, we introduce a spheroidal coordinate system that covers one complete asymptotically flat region and its adjacent ones, and allows the solution to be expressed in a simple form.