Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations
  It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented. 
Lode Wylleman
gr-qc