Ricci and matter collineations of locally rotationally symmetric space-times

TL;DR

The paper introduces a new method to determine Ricci and Matter Collineations in certain symmetric spacetimes, simplifying the process by relating it to known Killing vectors, and applies it to specific locally rotationally symmetric models.

Contribution

A novel method for finding Ricci and Matter Collineations that reduces the problem to determining Killing vectors, applied to locally rotationally symmetric spacetimes.

Findings

Identified all hypersurface homogeneous LRS spacetimes with proper RCs and MCs.

Derived the explicit collineation vectors for these spacetimes.

Provided a systematic approach to analyze symmetries in non-degenerate Ricci and energy-momentum tensors.

Abstract

A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors.