On the definition of matter collineations

TL;DR

This paper investigates the symmetries of the stress-energy tensor in spacetimes, revealing conditions under which matter collineations form infinite-dimensional Lie algebras, with implications for understanding spacetime symmetries.

Contribution

It extends previous results by characterizing matter collineations for diagonal stress-energy tensors in mixed form and generalizes to broader second rank tensors.

Findings

Infinite-dimensional Lie algebras of collineations for diagonal tensors

Finite-dimensional cases occur when the tensor depends on all coordinates

Extension of results to more general second rank tensors

Abstract

It is shown that when the stress-energy tensor of a spacetime is diagonal and is written in the mixed form, its collineations admit infinite dimensional Lie algebras except possibly in the case when the tensor depends on all the spacetime coordinates. The result can be extended for more general second rank tensors.