Global aspects of shear‐free perfect fluids in general relativity

TLDR: In this article, it was shown that shear-free expanding irrotational perfect fluids obeying a barotropic equation of state p = p(μ) and satisfying the field equations of general relativity form three distinct classes.

Abstract: In an earlier investigation of the class of shear‐free expanding (or contracting) irrotational perfect fluids obeying a barotropic equation of state p=p( μ), and satisfying the field equations of general relativity, it was shown that the space‐times form three distinct classes. In one class, the fluid acceleration is zero (i.e., the flow is geodesic), and the space‐times are the well‐known spatially homogeneous and isotropic Friedmann–Robertson–Walker (FRW) models. In the other two classes, the acceleration is nonzero, and the space‐times are spatially anisotropic and are less familiar. One of these classes consists of the spherically symmetric Wyman solutions, whereas models that are plane symmetric, and either spatially or temporally homogeneous, constitute the final class. Analytic forms for these anisotropic space‐time metrics were given, although in each case their exact determination would depend upon the solution of a single nonlinear ordinary differential equation, which has not been achieved. The...