I read that an alcubierre drive would get destroyed by hawking radiation inside the warp bubble. Where does this hawking radiation come from? And why does it only happen to objects inside the bubble?
I've seen various articles on the subject, and I would guess they all stem from the paper Semiclassical instability of dynamical warp drives.
If you're in the centre of an Alcubierre drive at superluminal speeds it looks as if there is a white hole in front of you and a black hole behind you. This is because any light rays you send forward cannot escape from the bubble, while any light rays from the universe approaching you from the rear of the drive cannot enter the bubble.
There is probably Hawking/Unruh radiation associated with both horizons. I say probably because it's a semi-classical approximation and it's a hard calculation (disclaimer: I only skimmed it - most of it is beyond me!). The paper does the calculation in 1+1D space because it's too hard in 3+1D. Anyhow, the result of the calculation is that at superluminal speeds the radiation associated the the apparent horizons is intense enough to kill astronauts inside the drive.
The main interest of the paper is actually that the stress-energy tensor associated with the horizon at the front of the drive increases without limit once the drive starts moving, and the geometry is therefore unstable. If true, this means the drive would be destroyed as soon as it started moving. Cooking the occupants is just a by product of this.
I too have only read articles on the subject, but I think yes, because the forward and rear drives, but also because inside the warp bubble becomes flat. Anything inside (again, as I understand it) would be obliterated. And yes, radiation is just one consequence of the proposed drive.
Based upon my research of the topic, there are two factors that can cause heating. The first, and primary one, is that any object moving at superluminal speeds (or at least the space it is placed in) will take in any objects within its path (this is anything from cosmic dust to plasma and radiation). There is no limit to the amount of radiation that can be absorbed, but this would be approximately 10^64 kelvin for people inside of the bubble (this is also considering the Hawking Radiation mentioned in the first answer). But if the crew survive, all of this radiation shall be released upon the destination, thus, frying the destination upon entry in a supernova-type explosion. Another source of radiation could be the negative energy ring itself. This is weird because the negative energy it has increase the quantum energy of the vacuum, as this energy decreases the relative energy of one area of space, and the vacuum of space likes to stay at a certain energy (to over simplify the cosmological constant, Λ and the weak energy condition imbalance). Basically, if -100 joules existed in a region, 100 joules would rise in its place. This is like how photons focused in one area can cause the virtual particles of the quantum vacuum to decrease. For further reading, certain sites on the Wikipedia citations are very helpful in further explaining what happens.