Rotating solenoidal perfect fluids of Petrov type D
  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. 
Norbert Van den Bergh, Lode Wylleman