Covariant jump conditions in electromagnetism

A generally covariant four-dimensional representation of Maxwell’s electrodynamics in a generic material medium can be achieved straightfor-wardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which sat-isfy Maxwell’s equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differ-ential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are appli-cable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants