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Where $vb(t)$ is the arbitrary velocity of the bubble wall as a function of time, and $f(rs)$ is a suitable function that dictates the shape of the warp field, often described as a compact hyperbolic function centered around the spacecraft's spatial location.
Crucially, this mathematical framework does not require the spacecraft itself to move faster than light within its local reference frame; rather, the distance between the entry point and the destination is compressed in front of the bubble and expanded behind it. This mechanism is sometimes conceptually linked to the phenomenon descri…