If your ship just got trapped inside the event horizon of an super massive black hole, could the ship "accelerate" back out with an alcubierre drive?
Possibly, though you’d be escaping by moving the exit, potentially with hideously unintended side effects.
Basically below the event horizon of a black hole spacetime is warped such that nothing you do can alter anything above the black hole. Naturally this includes physical escape.
Alcubierre drives, on the other hand, work by warping spacetime such that you go from A to B without ever locally breaching the speed of light.
If you mix the two (and I have no maths to back me up here because nobody wants me to even think the phrase Alcubierre-Schwarzchild metric) it does weird things to time around the black hole, and may well require more energy than is present in the universe.
You’ll need some hefty hand waving to explain how your alcubierre drive functions in the first place; and if your ship has already fallen past the event horizon they you must somehow have A: explained away the tidal forces that should have torn your ship apart and B:have already dealt with the fact that from your ship’s point of view the heat death of the universe has already occurred by the time they reach the event horizon.
Wait. Back up. What?
Oh, yeah. As you approach the event horizon of a black hole time dilates. That’s why it’s impossible to escape: spacetime just wont let you, To an outside observer your ship will never breach the event horizon, instead it will become a smeared out, permanently frozen image of itself. From your point of view the universe will move faster and faster as you approach the black hole. Usually you’d be torn into incandescent plasma long before you got anywhere near close enough to see the universe end, but hey, handwaves.
So: now you’re not escaping from below the event horizon, but rather from just above it. This makes things easier, because an Alcubierre Drive (simply) expands space behind you and compresses it in front of you. Turning it on just above a black hole will ‘push’ the event horizon closer to the singularity below it, letting you get far enough ‘away’ to achieve escape velocity. Hooray!
Again: there’s some handwave here. Alcubierre drives (at least using the Alcubierre-White warp equations) act as more of a speed multiplier than a drive on their own, so you’ll need to deal with how you get enough energy to escape. Also: if you’re ‘in’ the black hole the amount of energy you’ll need to warp your way free will grow as you get closer to the black hole (sensibly, as you’ll be spending longer trying to escape).
Now for the unintended side effects.
Mathematically speaking if a black hole is spinning fast enough or has enough electric charge then it has no event horizon. This means you can see and interact with the singularity at the core of the black hole: a so-called ‘Naked Singularity’. Physicists and mathematicians don’t agree about what such a thing would look like because while it’s mathematically possible the one thing nature abhors more than a vacuum is a singularity. Our models of physics break down. Our models of mathematics break down. In many ways the feared ‘event horizon’ is a shield between us and pure unfettered ‘What?’. Nobody likes a naked singularity.
Again: I haven’t done the maths here because it’s fearsome, but if you ram enough power into your Alcubierre drive I can’t think of a reason why you would t be able to push the event horizon all the way back to the singularity - at which point my brain breaks. You also run hard into the 'Cosmic Censorship Hypothesis', which holds that naked singularities simply aren't allowed. You would be fighting the entire universe if you tried to create one.
So: you may well be able to escape the clutches of a black hole with your drive, as long as you have enough power. Just take care not to break physics.
Well, seeing how the event horizon is the area from where the escape velocity is equal to the speed of light; an alcubierre drive would indeed allow one to escape, by accelerating beyond escape velocity.
The problem is that deeper into the hole, the velocity required increases quickly, and the increased mass in the gravity well makes 'warping' it take more energy, so all an alcubierre drive would do is pushing the effective event horizon back.
J.J abrams got this right in his 'star trek' reboot; the enterprise wound up in a black hole, and even with their FTL, they could only prevent falling deeper. (star trek uses a style of FTL that works just like the alcubierre. in fact: it is the inspiration for the design)