Non-rigidly rotating stationary cylindrical dust spacetimes

TL;DR

This paper characterizes the unique non-rigidly rotating cylindrical dust spacetime with a regular axis, explores matching conditions to vacuum exteriors, and analyzes properties like vorticity and magnetic Weyl tensor components.

Contribution

It proves the uniqueness of Maitra's non-rigidly rotating solution, demonstrates matching to Weyl vacuum exteriors, and investigates physical properties such as vorticity and magnetic Weyl tensor presence.

Findings

Maitra spacetime is the unique non-rigidly rotating solution with a regular axis.

Non-rigidly rotating dust can be matched to Weyl vacuum exteriors, not Lewis class.

Non-rigid rotation implies non-zero vorticity and magnetic Weyl tensor.

Abstract

We consider stationary rotating cylindrically symmetric dust spacetimes. We first show that the Maitra spacetime is the unique non-rigidly (non null shear scalar) rotating solution with a regular axis and that is the most general one of the field equations. We are also able to demonstrate what Maitra's paper does not show, where the solution is merely stated without any demonstration. Then we find that the non-rigidly rotating spacetimes, not necessarily regular, can be matched, across timelike cylindrical hypersurfaces, to a one-parameter family of stationary vacuum exteriors given by the Weyl class but not to the Lewis class, generalizing a result by Bonnor and Steidman. Among other properties, it is shown that the amount of rotating dust packed inside a cylinder is bigger if it is rigidly rotating than non-rigidly rotating. Finally, we show that in the non-rigidly rotating cases the fluid necessarily has vorticity and the spacetimes are not silent, where the magnetic part of the Weyl tensor is non-zero.