Proper Matter Collineations of Plane Symmetric Spacetimes

TL;DR

This paper studies matter collineations in plane symmetric spacetimes with degenerate energy-momentum tensors, identifying cases with finite-dimensional symmetry groups including isometries and proper collineations.

Contribution

It classifies matter collineations in degenerate plane symmetric spacetimes, revealing finite-dimensional groups with specific numbers of symmetries.

Findings

Finite-dimensional matter collineation groups found in three cases.

Groups consist of four, six, or ten collineations.

Some collineations are isometries, others are proper.

Abstract

We investigate matter collineations of plane symmetric spacetimes when the energy-momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten in which four are isometries and the rest are proper.