Algebraic decomposition of the electromagnetic constitutive tensor. A step toward pre-metric based gravitation?

TL;DR

This paper explores an advanced algebraic decomposition of the electromagnetic constitutive tensor, aiming to deepen understanding of its principal part for potential applications in pre-metric gravitation theories.

Contribution

It introduces a more detailed algebraic decomposition of the principal part of the electromagnetic constitutive tensor, extending previous classifications.

Findings

Decomposition reveals new substructures within the principal part.

Enhanced understanding of tensor components may inform gravitational theories.

Provides a mathematical framework for further theoretical developments.

Abstract

It is known that the electromagnetic constitutive tensor can be algebraically decomposed in three parts: the so-called principal part, the axion part and the skewon part (see gr-qc/0506042). The aim of this paper is to provide a deeper decomposition of the principal part.