Narrow Results

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.

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

This study deals with the spherically symmetric radiating star (with dissipative perfect fluids) with a central vacuum cavity, evolving under the assumption of expansion-free motion. The analytical model of the such dynamics star is discussed in three regimes — diffusion approximation, geodesic motion and self-similarity — and the solutions of dynamical equations are obtained in its complete generality. The structure scalars, which are related to the fundamental properties of fluid distribution, are also discussed which played a very important role in the dynamics of cavity models. It has been shown that energy density is homogeneous but violates the energy condition under quasi-static diffusion approximation.