Some Properties of an Exact Solution for a Non-Static Uniform Density Sphere with Singularity in General Relativity

Abstract

A class of exact solutions for a time-dependent uniform density sphere is given. The model is non-regular since there exists an interior surface where the pressure is infinite. However, it is shown that this surface is always hidden by trapped surfaces. The equation for the zero pressure boundary of the fluid sphere is investigated, and it is found that this equation always has just one solution when integration constants are properly chosen. The pressure gradient is shown to be negative, and all models possesses the strange property that the circumference is not an increasing function of diameter. We also find that for contracting models the pressure is a decreasing function of time for the interior layers close to the singular surface. Two kinds of matter "velocities" are investigated, and it is found that just one of these is a decreasing function of radial coordinate.