Matter Inheritance Symmetries of Spherically Symmetric Static Spacetimes

TL;DR

This paper classifies spherically symmetric static spacetimes based on their matter inheritance symmetries, revealing conditions for finite and infinite dimensional symmetries and relating them to known geometric symmetries.

Contribution

It provides a complete classification of matter inheritance symmetries in spherically symmetric static spacetimes, including degenerate and non-degenerate energy-momentum tensors.

Findings

Degenerate case mostly yields infinite dimensional symmetries

Two cases with finite symmetries even when degenerate

Non-degenerate case also has finite symmetries

Abstract

In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static spacetimes by their matter inheritance symmetries. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional matter inheriting symmetries. It is worth mentioning here that two cases provide finite dimensional matter inheriting vectors even for the degenerate case. The non-degenerate case provides finite dimensional matter inheriting symmetries. We obtain different constraints on the energy-momentum tensor in each case. It is interesting to note that if the inheriting factor vanishes, matter inheriting collineations reduce to be matter collineations already available in the literature. This idea of matter inheritance collineations turn out to be the same as homotheties and conformal Killing vectors are for the metric tensor.