Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

TL;DR

This paper explores plane-symmetric inhomogeneous cosmological models with perfect fluids in general relativity, identifying new classes of solutions with shear and analyzing their properties systematically.

Contribution

It systematically investigates integrable solutions of Einstein's equations for shear-filled plane-symmetric perfect fluid models, revealing three new classes of solutions.

Findings

Shear solutions must be non-static.

Identified three classes of solutions with shear.

Provided systematic analysis of integrable cases.

Abstract

In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions.