Warp Drive: Alcubierre Metric Simulator

This simulator visualizes the Alcubierre warp metric, the 1994 general-relativity solution that moves a "bubble" of flat spacetime through the universe by contracting space ahead of it and expanding space behind it, rather than accelerating a ship through space in the ordinary sense. The colored field shows the volume-expansion scalar θ computed directly from the metric's shaping function f(r_s): red ahead of the bubble marks contraction, blue behind marks expansion, and the interior — where the ship actually sits — stays flat and undistorted. The warped grid overlay shows the same contraction/expansion pattern applied to a coordinate grid. Adjust bubble speed, radius and wall sharpness to see how a sharper, faster-moving bubble concentrates more extreme curvature into a thinner wall.