On the uniqueness of a shear-vorticity-acceleration-free velocity field in space-times

We prove that in space-times a velocity field that is shear, vorticity and acceleration - free, if any, is unique up to reflection, with these exceptions: generalized Robertson- Walker space-times whose space sub-manifold is warped, and twisted space-times (the scale function is space-time dependent) whose space sub-manifold is doubly twisted. In space-time dimension n = 4, the Ricci and the Weyl tensors are specified, and the Einstein equations yield a mixture of two perfect fluids.