An exhaustive classification of aligned Petrov type D purely magnetic perfect fluids

TL;DR

This paper proves that all aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric and are explicitly known, providing a complete classification of these spacetimes.

Contribution

It establishes that such fluids are necessarily locally rotationally symmetric, confirming that all solutions are already explicitly known.

Findings

All aligned Petrov type D purely magnetic perfect fluids are locally rotationally symmetric.

These fluids are explicitly known solutions.

The classification is exhaustive and complete.

Abstract

We prove that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric and hence are all explicitly known.