Lie symmetries of the energy-momentum tensor for plane symmetric static spacetimes

TL;DR

This paper investigates matter collineations in plane symmetric static spacetimes, providing explicit forms and Lie algebra structures, and compares these symmetries with Ricci and Killing vectors to understand their relationships.

Contribution

It presents explicit forms of matter collineations and their Lie algebra for plane symmetric static spacetimes, and compares them with Ricci and Killing vectors.

Findings

MCs have been explicitly derived for specific spacetimes.

MCs are generally independent of RCs and KVs.

Examples show MCs do not contain RCs or KVs in general.

Abstract

Matter collineations (MCs) are the vector fields along which the energy-momentum tensor remains invariant under the Lie transport. Invariance of the metric, the Ricci and the Riemann tensors have been studied extensively and the vectors along which these tensors remain invariant are called Killing vectors (KVs), Ricci collineations (RCs) and curvature collineations (CCs), respectively. In this paper plane symmetric static spacetimes have been studied for their MCs. Explicit form of MCs together with the Lie algebra admitted by them has been presented. Examples of spacetimes have been constructed for which MCs have been compared with their RCs and KVs. The comparison shows that neither of the sets of RCs and MCs contains the other, in general.