Plane Wave Scattering by a PEC Wedge in Relativistic Translational Motion: Exact and Uniform Asymptotic Solutions

The study of fast-moving scatterers has received much attention due to its fundamental applications for modern radio astronomy and radar problems. This kind of problem relies on solving complicated time-dependent boundary conditions and only the wave phenomena associated with simplified scattering scenarios are today completely deep-seated. In this paper, a novel solution for the scattering of plane waves by a perfectly electrically conducting (PEC) wedge in motion is introduced on the grounds of Einstein's special theory of relativity. The exact solution for the 3D vector problem of an arbitrarily polarized time-harmonic plane wave excitation is obtained in closed form. In addition, a solution based on the uniform asymptotic theory (UAT) ansatz is obtained, rendering this approach a promising framework for modeling several relativistic effects of other complex-shaped and fast-moving objects.