Science of Discworld III

Schwarzschild radius for the Sun is 1.2 miles (2 km), and for the Earth 0.4 inches (1 cm) – both buried inaccessibly deep where they can’t cause trouble. So it wasn’t entirely clear how significant the strange mathematical behaviour was … or even what it meant.
    What would happen to a star that is so dense that it lies inside its own Schwarzschild radius?
    In 1939 Robert Oppenheimer and Hartland Snyder showed that it would collapse under its own gravitational attraction. Indeed a whole portion of spacetime would collapse to form a region from which no matter, not even light, could escape. This was the birth of an exciting new physical concept. In 1967 John Archibald Wheeler coined the term black hole , and the new concept was christened.
    How does a black hole develop as time passes? An initial clump of matter shrinks to the Schwarzschild radius, and then continues to shrink until, after a finite time, all the mass has collapsed to a single point, called a singularity. From outside, though, we can’t observe the singularity: it lies beyond the ‘event horizon’ at the Schwarzschild radius, which separates the observable region, from which light can escape, and the unobservable region where the light is trapped.
    If you were to watch a black hole collapse from outside, you would see the star shrinking towards the Schwarzschild radius, but you’d never see it get there. As it shrinks, its speed of collapse as seen from outside approaches that of light, and relativistic time-dilation implies that the entire collapse takes infinitely long when seen by an outside observer. The light from the star would shift deeper and deeper into the red end of the spectrum. The name should be ‘red hole’.
    Black holes are ideal for spacetime engineering. You can cut-and-paste a black hole into any universe that has asymptotically flat regions, such as our own. 1 This makes black hole topology physically plausible in our universe. Indeed, the scenario of gravitational collapse makes it even more plausible: you just have to start with a big enough concentration of matter, such as a neutron star or the centre of a galaxy. A technologically advanced society could build black holes.
    A black hole doesn’t possess CTCs, though, so we haven’t achieved time travel. Yet. However, we’re getting close. The next step uses the time-reversibility of Einstein’s equations: to every solution there corresponds another that is just the same, except that time runs backwards. The time reversal of a black hole is called a white hole. A black hole’s event horizon is a barrier from which no particle can escape; a white hole’s event horizon is one into which no particle can fall, but from which particles may emerge at any moment. So, seen from the outside, a white hole would appear as the sudden explosion of a star’s worth of matter, coming from a time-reversed event horizon.
    White holes may seem rather strange. It makes sense for an initial concentration of matter to collapse, if it is dense enough, and thus to form a black hole; but why should the singularity inside a white hole suddenly decide to spew forth a star, having remained unchanged since the dawn of time? Perhaps because time runs backwards inside a white hole, so causality runs from future to past? Let’s just agree that white holes are a mathematical possibility, and notice that they too are asymptotically flat. So if you knew how to make one, you could glue it neatly into your own universe, too.
    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 tubein 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.
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