Ray trajectories for Alcubierre spacetime

TL;DR

This paper models ray trajectories in an Alcubierre spacetime analogue using a Tamm medium, revealing evanescent wave regions, sensitivity to warp bubble velocity, and focusing effects at high speeds.

Contribution

It provides a detailed geometric-optics analysis of ray paths in a Tamm medium simulating Alcubierre spacetime, highlighting new wave propagation phenomena.

Findings

Evanescent waves occur near the warp bubble region.

Ray trajectories are highly sensitive to warp bubble velocity.

Warp bubble acts as a focusing lens at high speeds.

Abstract

The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are ontinuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a focusing lens, most notably at high speeds.