Rotating solenoidal perfect fluids of Petrov type D

TL;DR

This paper proves that certain Petrov type D perfect fluids with specific vorticity and Weyl tensor properties are either purely electric or exhibit local rotational symmetry, providing explicit metrics for the latter case.

Contribution

It establishes a classification result for Petrov type D perfect fluids under specific conditions, including explicit LRS metric solutions.

Findings

Aligned Petrov type D perfect fluids are either purely electric or LRS.

Explicit LRS metrics are derived.

Conditions on vorticity and Weyl tensor divergence are crucial.

Abstract

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.