Not only that: you can glue a black hole and a white hole together. Cut them along their event horizons, and paste along these two horizons. The result is a sort of tube. Matter can pass through the tube
[1] This is a mathematician's way of saying that you can put a black hole anywhere you want. (Or, like a gorilla in a Mini, it can go anywhere it wants.)
in one direction only: into the black hole and out of the white. It's a kind of matter-valve. The passage through the valve follows a timelike curve, because material particles can indeed traverse it.
Both ends of the tube can be glued into any asymptotically flat region of any spacetime. You could glue one end into our universe, and the other end into somebody else's; or you could glue both ends into ours - anywhere you like except near a concentration of matter. Now you've got a wormhole. The distance through the wormhole is very short, whereas that between the two openings, across normal spacetime, can be as big as you like.
A wormhole is a short cut through the universe. But that's matter-transmission, not time travel. Never mind: we're nearly there.
The key to wormhole time travel is the notorious twin paradox, pointed out by the physicist Paul Langevin in 1911. Recall that in relativity, time passes more slowly the faster you go, and stops altogether at the speed of light. This effect is known as time dilation. We quote from The Science of Discworld: Suppose that Rosencrantz and Guildenstem are born on Earth on the same day. Rosencrantz stays there all his life, while Guildenstem travels away at nearly lightspeed, and then turns round and comes home again. Because of time dilation, only one year (say) has passed for Guildenstern, whereas 40 years have gone by for Rosencrantz. So Guildenstern is now 39 years younger than his twin brother.
It's called a paradox because there seems to be a puzzle: from Guildenstern's frame of reference, it is Rosencrantz who has whizzed off at near-lightspeed. Surely, by the same token, Rosencrantz should be 39 years younger, not Guildenstern? But the apparent symmetry is fallacious. Guildenstern's frame of reference is subject to acceleration and deceleration, especially when he turns round to head for home; Rosencrantz's isn't. In relativity, accelerations make a big difference.
In 1988 Michael Morris, Kip Thorne, and Ulvi Yurtsever realised that combining a wormhole with the twin paradox yields a CTC. The idea is to leave the white end of the wormhole fixed, and to zigzag the black one back and forth at just below the speed of light. As the black end zigzags, time dilation comes into play, and time passes more slowly for an observer moving with that end. Think about world-lines that join the two wormholes through normal space, so that the time experienced by observers at each end are the same. At first those lines are almost horizontal, so they are not timelike, and it is not possible for material particles to proceed along them. But as time passes, the line gets closer to the vertical, and eventually it becomes timelike. Once this `time barrier' is crossed, you can travel from the white end of the wormhole to the black through normal space - following a timelike curve. Because the wormhole is a short cut, you can do so in a very short period of time, effectively travelling instantly from the black end to the corresponding white one. This is the same place as your starting point, but in the past.
You've travelled in time.
By waiting, you can close the path into a CTC and end up at the same place and time that you started from. Not back to the future, but forward to the past. The further into the future your starting point is, the further back in time you can travel from that point. But there's one disadvantage of this method: you can never travel back past the time barrier, and that occurs some time after you build the wormholes. No hope of going back to hunt dinosaurs. Or to tread on Cretaceous butterflies.
Could we really make one of these devices? Could we really get through the wormhole?
There are other time machines based on the twin paradox, but all of them are limited by the speed of light. They would work better, and perhaps be easier to build and operate, if you could follow Star Trek and engage your warp drive, travelling faster than light.
But relativity forbids that, right?
Wrong.
Special relativity forbids that. General relativity, it turns out, permits it. The amazing thing is that the way it permits it turns out to be standard SF gobbledegook, invoked by innumerable writers who knew about relativistic limitations but still wanted their starships to travel faster than light. `Relativity forbids matter travelling faster than light,' they would incant, `but it doesn't forbid space travelling faster than light.' Put your starship in a region of space, and leave it stationary relative to that region. No violation of Einstein there. Now move the entire region of space, starship inside, with superluminal (faster-than-light) speed. Bingo!
Ha-ha, most amusing. Except ...
In the context of general relativity, that's exactly what Miguel Alcubierre Moya came up with in 1994. He proved that there exist solutions of Einstein's field equations involving a local `warping' of spacetime to form a mobile bubble. Space contracts ahead of the bubble and expands behind it. Put a starship inside the bubble, and it can 'surf' a gravitational wave, cocooned inside a static shell of local spacetime. The speed of the starship relative to the bubble is zero. Only the bubble's boundary moves, and that's just empty space.
The SF writers were right. There is no relativistic limit to the speed with which space can move.
Warp drives have the same drawback as wormholes. You need exotic matter to create the gravitational repulsion needed to distort spacetime in this unusual way. Other schemes for warp drives have been proposed, which allegedly overcome this obstacle, but they have their own drawbacks. Sergei Krasnikov noticed one awkward feature of Alcubierre's warp drive: the inside of the bubble becomes causally disconnected from the front edge. The starship's captain, inside the bubble, can't steer it, and she can't even turn it on or off. He proposed a different method, a 'superluminal highway'. On the outward trip, the starship travels below lightspeed and leaves a tube of distorted spacetime behind it. On the way back, it travels faster than light along the tube. The superluminal highway also needs negative energy; in fact, Ken Olum and others have proved that any type of warp drive does.
There are limits to the lifetime of any given amount of negative energy. For wormholes and warp drives these limits imply that such structures must either be very small, or else the region of negative energy must be extremely thin. For example, a wormhole whose mouth is three feet (1m) across must confine its negative energy to a band whose thickness is one millionth of the diameter of a proton. The total negative energy required would be equivalent to the total output (in positive energy) of 10 billion stars for one year. If the mouth were one light year across, then the thickness of the negative energy band would still be smaller than a proton, and now the negative energy requirement would be that of 10 quadrillion stars.
Warp drives, if anything, are worse. To travel at 10 times lightspeed (a mere Star Trek Warp Factor 2) the thickness of the bubble's wall must be 10-32 metres. If the starship is 200 yards (200m) long, the energy required to make the bubble has to be 10 billion times the mass of the known universe.