Rainich theory applied to m-rank tensors in n-dimensions

TL;DR

This paper develops a tensorial-computational method to determine when an m-rank tensor in any dimension can represent an energy-momentum tensor of a physical field, applying it to various field types and examples.

Contribution

It introduces a new tensorial-computational approach to identify algebraic conditions for m-rank tensors to be energy-momentum tensors in arbitrary dimensions.

Findings

Method successfully applied to electromagnetic, scalar, and perfect fluid tensors.

Provides algebraic conditions for m-rank tensors to be energy-momentum tensors.

Demonstrates application of Rainich theory to specific tensor examples.

Abstract

We show a tensorial-computational way to find out conditions that must fulfil an m-rank tensor in arbitrary dimension in order to be algebraically the energy-momentum tensor of some field. We apply in this paper our method to three 2-rank tensors: electromagnetic, mass less scalar field and perfect fluid tensors. Finally we apply the Rainich theory to some examples.