Multi-Sheet Wormholes in the Gravitational Soliton Formalism

TL;DR

This paper constructs static, regular wormhole solutions connecting multiple regions using a novel multi-sheet gravitational soliton approach supported by phantom scalar fields.

Contribution

It introduces a new method of creating multi-sheet wormhole solutions by gluing sheets in the gravitational soliton formalism, extending previous single-sheet models.

Findings

Successfully constructed multi-sheet wormhole geometries.

Demonstrated regularity and stability of the solutions.

Extended the gravitational soliton formalism to multi-region wormholes.

Abstract

We analytically construct static regular solutions describing wormholes that connect multiple asymptotic regions, supported by a phantom scalar field. The solutions are static and axially symmetric, and are constructed using the gravitational soliton formalism, in which the equations of motion reduce to the Laplace equations on a two-dimensional sheet. However, the presence of multiple asymptotic regions necessitates the introduction of multiple such sheets. These sheets are appropriately cut and glued together to form a globally regular geometry. This gluing procedure represents the principal distinction from conventional Weyl-type solitonic solutions and is a characteristic feature of the wormhole geometries studied in this paper.