Spacelike Motion inside a Closed Null Surface Generated by Abelian Electromagnetic Gauge Transformations

It has been proven previously that Abelian electromagnetic gauge transformations can create a region in spacetime surrounded by a null surface such that inside the surface spacetime undergoes a timelike-spacelike reflection. Therefore, timelike intervals will turn into spacelike intervals inside the null surface and vice versa. We will use this property in order to prove that such a closed region will be able to undergo faster than the speed of light motion in a four-dimensional Einstein–Maxwell or Maxwell–Minkowski spacetimes.