symmetries of the Ricci tensor of static space times with maximal symmetric transverse spaces

TL;DR

This paper classifies static spacetimes with maximally symmetric transverse spaces based on Ricci collineations, identifying the number of collineations and discovering new metrics with proper Ricci collineations.

Contribution

It provides a detailed classification of Ricci collineations in these spacetimes and introduces new metrics with proper Ricci collineations.

Findings

Admitted Ricci collineations are ten, seven, six, or four.

Identified new metrics with proper Ricci collineations.

Analyzed non-degenerate Ricci tensors in these spacetimes.

Abstract

Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor ($det.(R_{\alpha}) \neq 0$). It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. Some new metrics admitting proper Ricci collineations are also investigated.