Plane symmetric cosmological models

TL;DR

This paper applies Lie symmetry analysis to Einstein-Maxwell equations in plane symmetric spacetime, deriving exact solutions that describe the universe's evolution with electromagnetic fields and analyzing their physical and geometrical properties.

Contribution

It introduces a novel application of Lie symmetry methods to inhomogeneous electromagnetic cosmological models with plane symmetry, providing new exact solutions.

Findings

Electromagnetic field tensor increases over time.

Exact solutions describe universe evolution with electromagnetic fields.

Physical and geometrical features of specific models are discussed.

Abstract

In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the similarity reductions and obtain exact solutions in connection to the evolutionary scenario of the universe. The special feature of the study is that it deals with the electromagnetic energy of the inhomogeneous universe through the non-vanishing component of electromagnetic field tensor $F_{12}$ and assumes that the free gravitational field is of Petrov type-II non-degenerate. We have found that the electromagnetic field tensor is positive and increasing function of time. To validate the solution set, we examine with detailed discussions several physical as well as geometrical features of a specific sub-case of the model.