Extended Einstein-Maxwell model

TL;DR

This paper develops a comprehensive extended Einstein-Maxwell model for relativistic media with polarization and magnetization, incorporating transient thermodynamics and providing an exact cosmological solution with hidden electromagnetic fields.

Contribution

It introduces a phenomenological extended constitutive framework for electrodynamics in relativistic media, including higher-order derivatives and a modified stress-energy tensor.

Findings

Derived exact solution for an isotropic cosmological model with electromagnetic fields.

Formulated extended constitutive equations considering transient thermodynamics.

Proposed a modified stress-energy tensor for electromagnetic fields in media.

Abstract

A self-consistent extended Einstein-Maxwell model for relativistic non-stationary polarizable-magnetizable anisotropic media is presented. Based on the analogy with relativistic extended irreversible (transient) thermodynamics, the extended constitutive equations for the electrodynamics of continua are formulated phenomenologically, the convective derivatives of the first, second, etc. orders being taken into account. The master equations for the gravity field contain a modified effective (symmetric) stress-energy tensor of the electromagnetic field in a material medium, the use of this tensor being motivated both by historical analogies and direct variational procedure. By way of example we consider the exact solution of the extended Einstein-Maxwell model, describing the isotropic cosmological model with hidden non-vanishing electromagnetic field, electric polarization and magnetization.