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Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

Des J. Mc Manus·Alan A. Coley
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Abstract

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(μ)$, with $\frac{dp}{dμ} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

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Des J. Mc Manus, Alan A. Coley. 1994-05-16. Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies. https://doi.org/10.1088/0264-9381%2F11%2F8%2F011

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