On an alignment condition of the Weyl tensor
The authors consider a perfect fluid spacetime with purely magnetic or purely electric Weyl tensor and prove that the fluid 4-velocity vector at any point lies in the 2-plane spanned by the principal null directions of the Weyl tensor. This is a generalization of the result obtained by A. Barnes and R. R. Rowlingson. They apply this result to Petrov type D shear-free perfect fluid solutions of the Einstein equation and prove that in the purely magnetic case the solution is locally rotationally symmetric.
scientific article; zbMATH DE number 1788509
scientific article