All cloaks are spacetime cloaks

Abstract

Most invisibility cloaks designed with the transformation optics approach have used purely spatial transformations. When viewed from a 4-dimensional perspective it becomes obvious that purely spatial cloak transformations introduce unwanted effects such as space-like trajectories of light. By considering time transformations in conjunctions with spatial transformations, it may be possible to mitigate these unwanted effects. This demonstrates the importance of 4-dimensional thinking for transformation optics.