Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

TL;DR

This paper investigates a class of anisotropic fluid cosmological models in general relativity that are shear-free, irrotational, and geodesic, providing new insights into their metric forms, stress tensors, and possible spacetime foliations.

Contribution

It establishes general results on the metric and stress tensor forms for these models and classifies both homogeneous and inhomogeneous solutions, including simple generalizations of isotropic cosmologies.

Findings

Models admit foliation by hypersurfaces of constant Ricci scalar.

Both spatially homogeneous and inhomogeneous models are constructed.

A classification scheme for these anisotropic fluid models is developed.

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 $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, 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.