# Cylindrical Systems in General Relativity

## TL;DR

This paper reviews cylindrical solutions in general relativity, discussing their properties, extensions, and implications for phenomena like jets, wormholes, and gravitational waves, clarifying misconceptions in the literature.

## Contribution

It provides a comprehensive review of cylindrical systems in Einstein's theory, including solutions, properties, and corrections to previous claims.

## Key findings

- Analysis of Levi-Civita and Lewis solutions and their extensions
- Clarification of the generality of cylindrically symmetric spacetimes
- Discussion of phenomena like jets, wormholes, and gravitational waves

## Abstract

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein's field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and Hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes.