Ricci Collineations for Non-Degenerate, Diagonal and Spherically Symmetric Ricci Tensors

TL;DR

This paper derives the form of Ricci collineation vector fields for non-degenerate, diagonal, spherically symmetric Ricci tensors, classifying them into 64 families based on derivatives of Ricci components.

Contribution

It provides explicit expressions for Ricci collineation vectors in this specific geometric setting, expanding understanding of symmetries in such spacetimes.

Findings

Classifies Ricci collineations into 64 families

Provides explicit formulas for collineation vectors

Illustrates methods with examples

Abstract

The expression of the vector field generator of a Ricci Collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector.