Massive-photon electrodynamics and MHD in curved spacetime and cosmology
Jai-chan Hwang, Hyerim Noh
TL;DR
The paper develops a comprehensive framework for massive-photon electrodynamics and MHD in curved spacetime, incorporating a Proca mass term through covariant Maxwell equations and an ADM 3+1 formulation. It provides Maxwell and MHD equations in both covariant and ADM forms, extends them to linearly perturbed Friedmann cosmology, and clarifies gauge transformation properties of EM fields and the vector potential, including wave equations with a Klein-type mass term. A key result is that, in the nonrelativistic limit via Klein and Madelung transformations, the dark Proca field behaves as vector dark matter with dust-like background and a calculable Jeans scale, linking photon mass to cosmological structure formation. The framework predicts mass-induced screening and damping of magnetic fields on super-Compton scales, enabling potential astrophysical and cosmological constraints on the photon mass from magnetic-field observations and vector DM phenomenology. Overall, the work extends relativistic MHD to massive photons in curved spacetimes and establishes a robust basis for exploring observational consequences in astrophysics and cosmology.
Abstract
We study a massive-photon electrodynamics and magnetohydrodynamics (MHD) in the curved spacetime of Einstein's gravity. We consider a Proca-type photon mass and present equations in terms of electric and magnetic (EM) fields and the vector potential. We present the electrodynamics and MHD in the covariant and ADM formulations valid in general spacetime and in linearly perturbed cosmological spacetime. We present wave equations assuming the metric variations are negligible compared with the field variations. Equations are derived without fixing the temporal gauge condition and the gauge transformation properties of the EM fields and the vector potential are presented. Using the post-Newtonian approximation we show the dark Proca field behaves as dust in the non-relativistic limit under the Klein transformation.