Ricci Collineations in Friedmann-Robertson-Walker Spacetimes

TL;DR

This paper investigates Ricci collineations in Friedmann-Robertson-Walker spacetimes, revealing maximal symmetry groups and classifying special cases with additional collineations, providing explicit forms of symmetry vectors.

Contribution

It provides a comprehensive classification of Ricci and matter collineations in FRW spacetimes, including explicit forms and special case analyses.

Findings

Maximal 15-parameter Ricci inheritance collineation group

Six-dimensional Ricci collineation group coincides with isometries

Infinite-dimensional groups for degenerate Ricci tensor cases

Abstract

Ricci collineations and Ricci inheritance collineations of Friedmann-Robertson-Walker spacetimes are considered. When the Ricci tensor is non-degenerate, it is shown that the spacetime always admits a fifteen parameter group of Ricci inheritance collineations; this is the maximal possible dimension for spacetime manifolds. The general form of the vector generating the symmetry is exhibited. It is also shown, in the generic case, that the group of Ricci collineations is six-dimensional and coincides with the isometry group. In special cases the spacetime may admit either one or four proper Ricci collineations in addition to the six isometries. These special cases are classified and the general form of the vector fields generating the Ricci collineations is exhibited. When the Ricci tensor is degenerate, the groups of Ricci inheritance collineations and Ricci collineations are infinite-dimensional. General forms for the generating vectors are obtained. Similar results are obtained for matter collineations and matter inheritance collineations.