  A generally covariant four-dimensional representation of Maxwell's
electrodynamics in a generic material medium can be achieved straightforwardly
in the metric-free formulation of electromagnetism. In this setup, the
electromagnetic phenomena described by two tensor fields, which satisfy
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 differential 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 applicable 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.
