On fluid spheres of uniform density in general relativity

Abstract

It is shown that for spherically symmetric perfect fluid solutions, with spatial isotropy and uniform density, the free gravitational fieldproduces a singularity at the centre of the sphere and when this singularity is removed the space-time is conformally flat.It is pointed out that the interior geometry of the fluid spheres with uniform density given by Thompson and Whitrow, and others, is conformally flat, and hence the spacetime is of class one.