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Assuming that the ship has all the energy needed, how is it supposed to supply the energy to sustain the bubble if nothing can reach the front horizon?
Consider a related question: "how is a black hole able to sustain an event horizon around itself if nothing can reach the horizon from within -- or even leave the singularity in the first place?"
That's a common way to answer this question and make it seem like it isn't an issue, but there's actually a lot of subtlety to it. In fact, according to the outside universe, the inside of a black hole doesn't exist
. All events at the horizon take place infinitely far in the future, and events in the interior are never observed.If we're outside, the properties of the event horizon and external gravitational field appear because to us there is a spherical shell of mass frozen on the horizon, and the field from a spherical shell is the same on the outside as if it were a singularity instead. Only when we shift into the reference frame which is falling into it do we discover that the mass has collapsed to singularity and the space-time extends into that region.
So the black hole isn't really "sustaining" its event horizon from a singularity at all. There is no contact between the two. It just turns out that the gravitational field according to observers inside and outside happen to exactly match up, even though they have totally different ideas of where the mass is located.
General relativity suggests in this case to take a shortcut. Say that the mass "really is" at the central singularity, and then use the field equations to determine the geometry of the surrounding space-time. The equations insist that you'll get a black hole with an event horizon. To not have the horizon would violate the equations. So with the Alcubierre drive, we could similarly say that the equations demand that this particular mass-energy distribution must create this space-time geometry with horizons around it. But we must also remember that the Alcubierre solution was found by solving the equations backward. It started with the space-time geometry that has this FTL behavior, and then worked backward to find the mass-energy distribution that causes it. But it does not tell us how that distribution could actually be created, or how that Alcubierre space-time could be generated out of an initially typical space-time. We know the mass-energy that yields this solution is exotic and violates some energy conditions in physics (so it probably can't exist). It is also likely that even if it can exist, it may be impossible to actually get it into the required configuration. A common argument (though I have yet to see it demonstrated rigorously) is that, similarly to trying to build a wormhole, Hawking radiation would amplify as you approach the conditions necessary for the horizons and FTL behavior, and the thing destroys itself. Which kind of brings us full circle -- your initial suspicion that there is a problem with having the ship generate this field around itself from scratch is probably correct, but for less obvious reasons.