This paper shows that in general relativity space-time will admit three linearly independent spacelike Killing vectors if the cosmic matter is a perfect fluid with a functional relationship between pressure and density and the spacelike eigenvectors of the shear tensor are parallel transported along the world lines of the fluid. In the Newtonian case it is proved that for an irrotational motion of a fluid with pressure and density functionally related spatial uniformity of the matter distribution leads to the homogeneity of the velocity field.

• Received 5 September 1984

DOI:https://doi.org/10.1103/PhysRevD.31.1807