Covariant constitutive relations and relativistic inhomogeneous plasmas

The notion of a two-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in non-relativistic phenomena is generalized to accommodate the constraints required of a causal formulation in spacetimes with background gravitational fields. In particular the concepts of spatial material in-homogeneity and temporal non-stationarity are formulated within a fully covariant spacetime framework. This framework is illustrated by re-casting the Maxwell-Vlasov equations for a collisionless plasma in a form that exposes a 2-point electromagnetic susceptibility kernel in spacetime. This permits the establishment of a perturbative scheme for non-stationary inhomogeneous plasma configurations. Explicit formulae for the perturbed kernel are derived in both the presence and absence of gravita-tion using the general solution to the relativistic equations of motion of the plasma constituents. In the absence of gravitation this permits an analysis of collisionless damping in terms of a system of integral equations that reduce to standard Landau damping of Langmuir modes when the perturbation refers to a homogeneous station-ary plasma configuration. It is concluded that constitutive modelling in terms of a 2-point susceptibility kernel in a covariant spacetime framework offers a natural ex-tension of standard non-relativistic descriptions of simple media and that its use for describing linear responses of more general dispersive media has wide applicability in relativistic plasma modelling