# Dynamo-optically active media: New aspects of the Minkowski-Abraham controversy

## TL;DR

This paper investigates the Minkowski-Abraham controversy by analyzing electromagnetic energy flux in dynamo-optically active media using covariant formalism, revealing differences in energy flux vectors despite identical energy densities.

## Contribution

It introduces a covariant formalism for symmetric stress-energy tensors in dynamo-optically active media, providing new insights into the longstanding Minkowski-Abraham debate.

## Key findings

- Energy density scalars and pressure tensors coincide for both tensor versions.
- Energy flux four-vectors differ in general cases.
- The formalism applies to axionically active vacuum, isotropic moving dielectric, and dynamo-optically active media.

## Abstract

Based on the covariant variation formalism, two versions of the symmetric effective stress-energy tensor of the electromagnetic field in a dynamo-optically active relativistic media are reconstructed in the framework of the tetrad and aether paradigms, respectively. We show that the energy density scalars and pressure tensors coincide for both versions of the stress-energy tensors, however, the corresponding energy flux four-vectors happen to be different in general case. This mathematical fact adds new arguments into the 100-year-long discussion, which is called Minkowski-Abraham controversy and is connected with the correct definition of the electromagnetic energy flux in a continuous media. We consider three examples: first, the axionically active vacuum; second, the spatially isotropic moving dielectric medium; third, the dynamo-optically active medium. We discuss possible applications of the elaborated formalism.