On the passage of radiation through inhomogeneous, moving media. X. Ray and phase paths in arbitrary velocity fields

Derivation of the equations describing general phase and ray paths, seen by an inertial observer, when the medium through which the radiation is propagating is, in general, expanding, accelerating, and shearing, and the refractive index of the medium may be an arbitrary function of frequency, position, and local acceleration. Several models developed to account for the radiation observed from pulsars make use, either implicitly or explicitly, of media which are rapidly moving, rapidly accelerating, rapidly expanding, and/or highly sheared. It is therefore believed that the general equations developed may be of use in such models in helping to unravel the tangled skein of paths followed by radiation produced in and/or propagating through such media.