Some Characteristics of a Non-Static Uniform Density Sphere in General Relativity

Abstract

The characteristics of some particular models for a non-static uniform density sphere is investigated. The model is not conformally flat, and the pressure is positive and the pressure gradient is negative. For contracting models pressure, p, and density, ρ, are increasing functions of time, and so are the active mass and the Misner-Sharp-Hernandez mass-function. Two kinds of matter "velocities" are investigated, and it is found that they both are decreasing functions of radial coordinate and they are increasing during the contraction. We have found that the condition ρ > 3p is fulfilled when the sphere is large, and during that period the speed of sound is less than the speed of light. Furthermore, for all models it is shown that ρ < p inside the sphere during the last moments before collapse to singularity. It is possible to choose parameters to have models where the inequality ρ < p will hold for some layers of the sphere before the surface collapses inside the Schwarzschild surface. However, all models possess the strange property that the circumference is not an increasing function of diameter.