EVOLUTION OF EXPANSION-FREE SELF-GRAVITATING FLUIDS AND PLANE SYMMETRY

Abstract

We investigate some analytical models of the plane symmetric distribution of anisotropic fluid with vanishing expansion scalar. Darmois junction conditions, on both the internal and external hypersurfaces, are given. A relationship between the Weyl tensor and the matter variables is developed. We explore four families of solutions under expansion-free condition some of which indicate the presence of thin shell, while some others satisfy junction conditions. It is shown that the Skripkin model is incompatible with junction conditions in the plane symmetry.