Ohmura’s extended electrodynamics: Longitudinal aspects in general relativity

Jimenez and Maroto [Phys. Rev. D 83, 023514 (2011)] 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 [Prog. Theor. Phys. 16, 684 (1956)] and Woodside's uniqueness theorem [Am. J. Phys. 77, 438 (2009)] to general relativity. Our formulation results in a theory that applies to both the field- (E,B) and potential- (phi,A) domains. We establish a self-consistent, longitudinal wave-propagation theory for the microscopic longitudinal part of the electric field. 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. 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.