How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?

TL;DR

This paper explores how electromagnetic fields interact with various geometric aspects of gravity, such as metric, nonmetricity, torsion, and curvature, especially in the context of alternative gravitational theories and experimental tests.

Contribution

It provides a comprehensive analysis of the different mechanisms and theories describing electromagnetic coupling to diverse gravitational structures, including non-minimal and non-local couplings.

Findings

Electrodynamics based on charge and flux conservation does not inherently couple to gravity.

The coupling occurs through constitutive laws relating excitation and field strength.

Various coupling schemes, including non-minimal and non-local, are discussed.

Abstract

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein's gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity. A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell's equations expressed in terms of the excitation H=(D,H) and the field strength F=(E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H= functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.