A nonminimally coupled Einstein-Maxwell model in a non-Riemann space-time with torsion

TL;DR

This paper derives field equations for a nonminimally coupled Einstein-Maxwell model in a non-Riemannian space-time with torsion, expressing them via Riemannian quantities and linking torsion to electromagnetic invariants.

Contribution

It introduces a novel formulation of Einstein-Maxwell equations with nonminimal coupling in a torsioned space-time, incorporating an electromagnetic constitutive tensor.

Findings

Torsion is generated by gradients of electromagnetic invariants.

Field equations are expressed in terms of Riemannian quantities.

A new electromagnetic constitutive tensor is formulated.

Abstract

A system of field equations for an Einstein-Maxwell model with $RF^2$-type nonminimal coupling in a non-Riemannian space-time with a non-vanishing torsion is derived and the resulting field equations are expressed in terms of the Riemannian quantities based on a metric with a Lorentzian signature. The torsion is generated by the gradients of the electromagnetic field invariants. An electromagnetic constitutive tensor is introduced in the formulation of the field equations.