Expansion-Free Evolving Spheres Must Have Inhomogeneous Energy Density Distributions

TL;DR

This paper demonstrates that inhomogeneous energy density distributions are necessary for expansion-free spherically symmetric systems, challenging the consistency of certain models like Skripkin's with junction conditions.

Contribution

It proves that expansion-free conditions in spherically symmetric fluids require inhomogeneous energy densities, providing a complete integration example with dust.

Findings

Skripkin model is inconsistent with junction conditions

Expansion-free fluids must have inhomogeneous energy density

Complete solution provided for dust case

Abstract

In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.