Free-space relativistic low-frequency scattering by moving objects

The present study brings together two aspects of electromagnetic theory: the recently discussed low-frequency series expansions based on the concept of Consistent Maxwell Systems, and Einstein's Relativistic Electrodynamics. Combined, this facilitates the analysis of pertinent low-frequency scattering problems involving objects moving with arbitrary constant velocities in free space. The low-frequency series expansions start with leading terms that are prescribed by solutions of the vector Laplace equation, thus significantly simplifying the conventional analysis in terms of the Helmholtz wave equation. The method is demonstrated by deriving relativistically exact explicit results leading terms for perfectly conducting circular-cylindrical and spherical scatterers. The results apply to arbitrary reference frames where the objects are observed in motion. For simplicity of notation expressions are given in terms of spatiotemporal coordinates native to the object's rest-frame. Subsequent substitution of the Lorentz transformation for the coordinates is then a straightforward matter. Previous exact relativistic results for scattering by moving objects have demonstrated the existence of velocity induced mode coupling. It is shown that the low-frequency expansions used here display the same effects for various orders of the partial fields appearing in the series.