Ohmura’s extended electrodynamics: longitudinal aspects in general relativity

Jiménez and Maroto ((2011) Phys. Rev. D 83 , 023514) predicted that free-space, longitudinal electrodynamic waves can propagate in curved space-time, if the Lorenz condition is relaxed. The present work studies this possibility by combining and extending the original theory by Ohmura ((1956) Prog. Theor. Phys. 16 , 684) and Woodside’s uniqueness theorem ((2009) Am. J. Phys. 77 , 438) to general relativity. Our formulation results in a theory that applies to both the field- ( E , B ) and potential- (Φ, A ) domains. We establish a self-consistent, longitudinal wave-propagation theory for the microscopic longitudinal part of the electric field ( E L ). We first show that the product of the parameters used previously for the extension of classical electrodynamics can be expressed as a superposition of microscopic displacement modes, which are confined to the energy shell, ∣ ω ∣ =  cq . We then show that nonlinear electrodynamic mixing allows creation of longitudinal waves in the near-field region of a source. A propagator approach gives substantial physical insight into the emission process.