Topological geons with self-gravitating phantom scalar field

TL;DR

This paper classifies topological geons formed from self-gravitating phantom scalar fields, analyzing their properties and potential observational signatures through a detailed mathematical and physical study.

Contribution

It introduces a classification of topological geons with self-gravitating phantom scalar fields and explores their physical and observational characteristics.

Findings

Identified three types of geon spacetimes.

Provided simple examples illustrating each geon type.

Analyzed potential observational effects of geodesic motion near geons.

Abstract

A topological geon is the quotient manifold $M/Z_2$ where $M$ is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically flat solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.