Integrability Conditions for Irrotational Dust with a Purely Electric Weyl Tensor: A Tetrad Analysis

Details Integrability Conditions for Irrotational Dust with a Purely Electric Weyl Tensor: A Tetrad Analysis Integrability Conditions for Irrotational Dust with a Purely Electric Weyl Tensor: A Tetrad Analysis

1994-10-03

arxiv.org/abs/astro-ph/9410005v1

Phys.Rev. D52 (1995) 3406-3415

Astronomy and Astrophysics

Astrophysics

submitted to Physical Review D, 23 pages, Latex

Scientific paper

10.1103/PhysRevD.52.3406

All spacetimes for an irrotational collisionless fluid with a purely electric Weyl tensor, with spacetime curvature determined by the exact Einstein field 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).

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