Symmetries of the Energy-Momentum Tensor of Spherically Symmetric Lorentzian Manifolds

TL;DR

This paper classifies spherically symmetric Lorentzian manifolds based on their matter collineations, revealing the number of symmetries depending on whether the energy-momentum tensor is degenerate or non-degenerate.

Contribution

It provides a comprehensive classification of matter collineations in spherically symmetric spacetimes, including cases with degenerate and non-degenerate energy-momentum tensors, extending previous results.

Findings

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

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

Recovered previous results as special cases.

Abstract

Matter collineations of spherically Symmetric Lorentzian Manifolds are considered. These are investigated when the energy-momentum tensor is non-degenerate and also when it is degenerate. We have classified spacetimes admitting higher symmetries and spacetimes admitting SO(3) as the maximal isometry group. For the non-degenerate case, we obtain either {\it four}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. The results of the previous paper [1] are recovered as a special case. It is worth noting that we have also obtained two cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional, i.e. {\it four} or {\it ten}.