On a Class of Exact Spherically Symmetric Solutions to the Einstein Gravitational Field Equations

Abstract

This paper presents a development of a well-known class of Einstein gravitational fields which describe, in comoving coordinates, spherically symmetric perfect fluids with spatially uniform density but with nonuniform pressure. It is noted that the sign of the spatial curvature or these distributions may vary with time, in contrast with the situation for the uniform model theory used in most cosmological applications. It is shown, however, that this entails physically unacceptable behaviour of the fluid. In conclusion there is given a preliminary investigation of isolated fluid spheres, and a description of their noncovariant 'spatial geometry' is discussed.