Ray trajectories for Alcubierre spacetime

Abstract

The Alcubierre spacetime was simulated by means of a Tamm medium which isasymptotically identical to vacuum and has constitutive parameters which are continuousfunctions of the spatial coordinates. Accordingly, the Tamm medium is amenable tophysical realization as a micro- or nanostructured metamaterial. A comprehensivecharacterization of ray trajectories in the Tamm medium was undertaken, within thegeometric-optics regime. Propagation directions corresponding to evanescent waves wereidentified: these occur in the region of the Tamm medium which corresponds to the warpbubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity ofthe warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitiveto the magnitude and direction of the warp bubble’s velocity, but rather lesssensitive to the thickness of the transition zone between the warp bubble andits background. In particular, for rays which travel in the same direction as thewarp bubble, the latter acts as a focusing lens, most notably at high speeds.