Non-minimal coupling for the gravitational and electromagnetic fields: A general system of equations

TL;DR

This paper develops a new set of coupled equations for gravity and electromagnetism using a non-minimal, non-linear extension of the Einstein-Hilbert-Maxwell action, exploring properties of a three-parameter model family.

Contribution

It introduces a novel self-consistent framework for gravitational and electromagnetic fields based on a non-minimal extension of the standard action, including explicit solutions for spherically symmetric charged objects.

Findings

A three-parameter family of non-minimal linear models is analyzed.

Explicit description of static spherically symmetric charged objects within the model.

Demonstration that the susceptibility tensor proportional to the double-dual Riemann tensor yields consistent solutions.

Abstract

We establish a new self-consistent system of equations for the gravitational and electromagnetic fields. The procedure is based on a non-minimal non-linear extension of the standard Einstein-Hilbert-Maxwell action. General properties of a three-parameter family of non-minimal linear models are discussed. In addition, we show explicitly, that a static spherically symmetric charged object can be described by a non-minimal model, second order in the derivatives of the metric, when the susceptibility tensor is proportional to the double-dual Riemann tensor