Integrability conditions for irrotational dust with a purely electric Weyl tensor: A tetrad analysis.

All spacetimes for an irrotational collisionless uid with a purely electric Weyl tensor, with spacetime curvature determined by the exact Einstein eld equations, are shown to be integrable. These solutions include the relativistic generalisations 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). Subject headings: cosmology galaxies: clustering, formation hydrodynamics relativity exact solutions