Stationary Cylindrical Anisotropic Fluid

TL;DR

This paper derives the equations and conditions for stationary cylindrically symmetric anisotropic fluids, showing that purely electric solutions are static and no conformally flat stationary cylindrical fluids exist under these conditions.

Contribution

It provides a complete set of equations and conditions for physically meaningful stationary cylindrical fluids and demonstrates the non-existence of conformally flat solutions.

Findings

Purely electric solutions are necessarily static.

No conformally flat stationary cylindrical fluids satisfy the conditions.

The paper includes an example and calculations of Weyl tensor components.

Abstract

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown that purely electric solutions are necessarily static. Then, it is shown that no conformally flat stationary cylindrical fluid exits, satisfying regularity and matching conditions.