Exotic Matter Budget of a Warp Bubble (2D Cross-Section)

A 2D side-on companion to the 3D warp-bubble simulator: this is the exact z=0 slice through the same Alcubierre metric, rendered as a live heatmap of the negative energy density around the bubble wall. The panel numerically integrates that density over the full shell volume every time you move a slider and reports the total exotic-mass requirement |M| = E/c², compared against Jupiter, the Sun or the entire Milky Way. Adjust the bubble's velocity, radius and wall sharpness and watch how fast the requirement grows.