# Rotating cylinders with anisotropic fluids in general relativity

## TL;DR

This paper develops a method to find exact solutions in general relativity for rotating cylinders filled with anisotropic fluids, recovering known solutions and discovering new ones with various physical properties.

## Contribution

It introduces a general approach to obtain exact solutions with anisotropic fluid sources in cylindrically symmetric spacetimes, including novel solutions.

## Key findings

- Exact solutions for anisotropic fluids in cylindrical symmetry
- Recovery of known solutions like perfect fluids and cosmic strings
- New solutions with radiation flows along the axis

## Abstract

We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining exact solutions with such sources, where the main features are splitting of the Ricci tensor into static and rotational parts and using the harmonic radial coordinate. Depending on the values of $w_i$, it appears possible to obtain general or special solutions to the Einstein equations, thus recovering some known solutions and finding new ones. Three particular examples of exact solutions are briefly described: with a stiff isotropic perfect fluid ($p = \rho$), with a distribution of cosmic strings of azimuthal direction (i.e., forming circles around the $z$ axis), and with a stationary combination of two opposite radiation flows along the $z$ axis.