Matter and Ricci collineations

TL;DR

This paper investigates the symmetries of tensors like the energy-momentum and Ricci tensors, revealing conditions under which their symmetry groups are finite or infinite dimensional Lie algebras.

Contribution

It characterizes the infinitesimal symmetry transformations of symmetric tensors, including Ricci and energy-momentum tensors, highlighting cases with finite and infinite dimensional Lie algebras.

Findings

Most cases have finite dimensional Lie algebras of symmetries.

Some degenerate cases have infinite dimensional symmetry groups.

Symmetry groups may not always form Lie algebras.

Abstract

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra but also, in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra.