Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations

TL;DR

This paper classifies static plane symmetric spacetimes based on their matter collineations, revealing the number and nature of these symmetries in both degenerate and non-degenerate energy-momentum tensor cases.

Contribution

It provides a detailed classification of matter collineations for static plane symmetric spacetimes, including cases with degenerate and non-degenerate energy-momentum tensors, identifying the possible numbers of symmetries.

Findings

Non-degenerate case yields 4, 5, 6, 7, or 10 matter collineations.

Degenerate case can have 4, 6, or 10 matter collineations with finite-dimensional groups.

Identifies isometries and proper matter collineations in these spacetimes.

Abstract

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either {\it four}, {\it five}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either {\it four}, {\it six} or {\it ten