Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry

Abstract

We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding, while for positive time, it is collapsing. With the aid of graphical three-dimensional plots, it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally, the sound-speed index is computed and the fluid obeys the causality criterion. The non-static exact solution found may prove useful in the study of gravitational waves.