Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

TL;DR

This paper classifies spherically symmetric static spacetimes based on their matter collineations, revealing cases with finite groups even when the energy-momentum tensor is degenerate and identifying various numbers of collineations in non-degenerate cases.

Contribution

It provides a detailed classification of static spherically symmetric spacetimes according to matter collineations, including cases with degenerate energy-momentum tensors and different counts of independent collineations.

Findings

Finite matter collineation group with degenerate energy-momentum tensor.

Various numbers of independent matter collineations in non-degenerate cases.

Matter collineations coincide with Ricci collineations but have different constraints.

Abstract

The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either {\it four}, {\it five}, {\it six} or {\it ten} independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.