Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs Spacetimes

TL;DR

This paper classifies Ricci collineations in Bianchi I, III, and Kantowski-Sachs spacetimes, identifying new metrics and exploring their relation to isometries and contracted Ricci collineations.

Contribution

It provides a comprehensive classification of Ricci collineations for these spacetimes, including new metrics and their connection to isometries.

Findings

Identification of Ricci collineations for various components

Discovery of new metrics under specific conditions

Presentation of contracted Ricci collineations family

Abstract

Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs space- times are classified according to their Ricci collineation vector (RCV) field of the form (i)-(iv) one component of $\xi^a (x^b)$ is nonzero, (v)-(x) two components of $\xi^a (x^b)$ are nonzero, and (xi)-(xiv) three components of $\xi^a (x^b)$ are nonzero. Their relation with isometries of the space-times is established. In case (v), when $det(R_{ab}) = 0$, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci collineations (CRC) are presented.