  We consider an ideal invisibility cloak which is illuminated by monochromatic
light and which moves in vacuum at constant relativistic velocity with respect
to the common inertial frame of light source and observer. We show that, in
general, the moving cloak becomes detectable by image distortions and by
generating a broad frequency spectrum of the scattered light. However, for many
special combinations of incident light frequency, wave vector of light, and
cloak velocity, ideal cloaking remains possible. It becomes non-reciprocal
though. This means that light rays emitted by the light source arrive at the
observer as though they have travelled through vacuum, but they take completely
different paths after being retro-reflected at the observer position.
