General relativistic Lagrangian continuum theories -- Part II: electromagnetic fluids and solids with junction conditions

Abstract

We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of relativistic continua introduced in Part I to include polarization, magnetization, and general elastic-electromagnetic coupling through a unified energy functional. By exploiting spacetime and material covariance, the framework yields the corresponding spacetime and convective variational principles, together with transparent expressions for the stress-energy-momentum tensor and the covariant Euler-type balance equations governing nonlinear electromagnetic continua. Coupling to general relativity is naturally incorporated, and when the action is augmented with Gibbons-Hawking-York boundary terms, the gravitational and electromagnetic junction conditions follow directly from the variational formulation. The results provide a coherent foundation for modeling nonlinear electromagnetic continua in relativistic regimes, with relevance to astrophysical systems where relativistic continuum dynamics and electromagnetic fields are known to be strongly coupled, such as neutron-star crusts, magnetar flares, relativistic jets, and accretion disks. We also offer systematic connections with several formulations appearing in the existing literature.