# Cylindrical wormholes: a search for viable phantom-free models in GR

## TL;DR

This paper presents new cylindrical wormhole models in general relativity that are free from exotic matter and causality violations by joining internal solutions with flat external regions, ensuring the Weak Energy Condition is satisfied.

## Contribution

It introduces two novel, regular, asymptotically flat cylindrical wormhole models in GR that do not require exotic matter and avoid closed timelike curves.

## Key findings

- Models satisfy the Weak Energy Condition
- Models are free from closed timelike curves
- Achieve asymptotic flatness with internal matter and junction surfaces

## Abstract

The well-known problem of wormholes in general relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric space-times with rotation. However, for cylindrical wormhole solutions a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our Universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some surfaces $\Sigma_-$ and $\Sigma_+$ on different sides of the throat. The configuration then consists of three regions, the internal one containing a throat and two flat external ones. We discuss different kinds of source matter suitable for describing the internal regions of such models (scalar fields, isotropic and anisotropic fluids) and present two examples where the internal matter itself and the surface matter on both junction surfaces $\Sigma_\pm$ respect the WEC. In one of these models the internal source is a stiff perfect fluid whose pressure is equal to its energy density, in the other it is a special kind of anisotropic fluid. Both models are free from closed timelike curves. We thus obtain examples of regular twice asymptotically flat wormhole models in GR without exotic matter and without causality violations.