We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.

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Tilted homogeneous cosmological models

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.

Theorems on shear-free perfect fluids with their Newtonian analogues

We continue our previous investigation of shear‐free perfect fluids in general relativity, under the assumptions that the fluid satisfies an equation of state p=p(μ) with μ+p≠0, and that the vorticity and acceleration of the fluid are parallel (and possibly zero). We classify algebraically the set of such solutions into thirteen invariant nonempty cases. In each case, we investigate the allowed isometry groups and Petrov types, and invariantly characterize the special subcases that arise. We also show how the various subcases are related to each other and to the works of previous authors.

A class of shear‐free perfect fluids in general relativity. II

There is mounting evidence that general relativistic shear-free perfect fluids, obeying a barotropic equation of state with , are necessarily irrotational or non-expanding. This conjecture has been demonstrated in a number of particular cases, but a general proof is still lacking. In the tetrad-based approach two particular cases require a special treatment, namely = constant and = constant. A proof is given that the conjecture holds for each of these. In addition, a formalism is presented enabling one to deal with the more general case of a -law equation of state + constant.

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The shear-free perfect fluid conjecture

Raychaudhuri-type equations are written for a cosmological model filled with perfect fluid and obeying the equations of a self-creation theory recently proposed by G. A. Barber. In addition some general results on spatially homogeneous cosmological models are obtained. The Hawking-Penrose energy condition suggests that the singularity can be avoided in this theory.

Some general results in self-creation cosmologies

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S. Banerji

Papers

Homogeneous Cosmological Models without Shear