INTEGRABILITY CONDITIONS FOR IRROTATIONAL DUST WITH A PURELY ELECTRIC WEYL TENSOR - A TETRAD ANALYSIS

All spacetimes for an irrotational collisionless fluid with a purely electric Weyl tenser, with a spacetime curvature determined by the exact Einstein held equations, are shown to be integrable. These solutions include the relativistic generalizations of the Zeldovich solutions of Newtonian theory. Thus our result shows the consistency of various studies of ''silent'' universes (where such consistency was assumed rather than proved).