Matter Collineations of Plane Symmetric Spacetimes

TL;DR

This paper investigates matter collineations in plane symmetric spacetimes with non-degenerate energy-momentum tensors, identifying multiple cases with proper collineations and deriving solutions to Einstein's equations.

Contribution

It classifies matter collineations for a specific class of plane symmetric spacetimes and finds new solutions under certain constraints.

Findings

Multiple proper matter collineations identified (4, 5, 6, 7, 10)

Derived solutions to Einstein field equations under specific constraints

Expanded understanding of symmetries in plane symmetric spacetimes

Abstract

This paper is devoted to the study of matter collineations of plane symmetric spacetimes (for a particular class of spacetimes) when the energy-momentum tensor is non-degenerate. There exists many interesting cases where we obtain proper matter collineations. The matter collineations in these cases are {\it four}, \emph{five}, {\it six}, \emph{seven} and {\it ten} with some constraints on the energy-momentum tensor. We have solved some of these constraints to obtain solutions of the Einstein field equations.