In one minute

Santos-Pereira, Abreu and Ribeiro study the Alcubierre metric, in which a particle inside a warp bubble can travel arbitrarily faster than light globally while staying subluminal locally. General relativity allows exactly this combination of global superluminal and local subluminal motion. Because the metric was first proposed as a geometry without a source, they solve the Einstein equations for it with dust as the source. Every such solution with pressureless dust turns out to be a vacuum solution. These solutions link the Alcubierre metric to the Burgers equation for shock waves in an inviscid fluid, and the shock waves behave as plane waves.

Dust content solutions for the Alcubierre warp drive spacetime