Massive Wave Solutions to the Einstein-Maxwell Equations

We use gauge fixing to derive Proca equation from Maxwell’s classical electrodynamics in curved spacetime. Further restrictions on the gauge yield the Klein-Gordon equation for scalar bosons. The self-coupling of electromagnetic fields through spacetime curvature originates the inertia of wave packets for non-null field solutions, suggesting an electromagnetic origin of mass. We study the weak field limit of these solutions and prove that the electrovacuum can behave as a charged nonlinear optical medium.