Addendum: Symmetries of the energy-momentum tensor

TL;DR

This paper extends previous work on matter symmetries in various symmetric spacetimes by analyzing the Ricci tensor and discussing additional consequences and references.

Contribution

It provides new insights into Ricci tensor properties and completes the classification of matter symmetries in symmetric spacetimes.

Findings

Classification of matter symmetries for non-static and static spacetimes

Analysis of Ricci tensor consequences

Additional references and implications

Abstract

In recent papers [1-3], we have discussed matter symmetries of non-static spherically symmetric spacetimes, static plane symmetric spacetimes and cylindrically symmetric static spacetimes. These have been classified for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. Here we add up some consequences and the missing references about the Ricci tensor.