Light propagation and intensity transport in metric-affine geometry

Abstract

We study electromagnetic wave propagation in metric--affine geometries, where torsion and non-metricity may be present and the coupling between electromagnetism and spacetime is no longer unique. Rather than choosing a particular coupling prescription a priori, we construct electromagnetic sectors that preserve standard $U(1)$ gauge invariance and projective invariance of the affine connection as guiding symmetry principles. We introduce two representative models, one in which the Maxwell term is dressed by a scalar prefactor built from non-Riemannian invariants, and another in which the kinetic term is modified by a rank--four constitutive tensor acting as an anisotropic medium. We derive their geometric--optics limits and show that their couplings can modify the effective light cone, change the relation between field amplitude and intensity, induce polarization-dependent propagation, and generate birefringence and mode mixing. These results thus provide the formal basis for a broader phenomenological study connecting torsion and non-metricity with electromagnetic observables in concrete metric--affine backgrounds, including black-hole imaging, birefringent lensing, polarization observables, and departures from photon-number conservation.