January 2, 2001 By MARK HAW

Black light at the end of the quantum tunnel

Black holes are supermassive collapsed stars. They are called 'black' because gravity inside the black hole is so strong that even light cannot escape.

Oh yes it can, said celebrated physicist Stephen Hawking a quarter of a century ago. Hawking's mathematical gymnastics showed that black holes could radiate light or particles — hence the eponymous 'Hawking radiation'.

End of story? Not quite, announce Maulik Parikh of the Spinoza Institute in the Netherlands and Frank Wilczek of Princeton's Institute for Advanced Study. The maths, they claim, never quite matched the 'pictorial' description of how Hawking radiation works, as glibly propounded by science writers and pub intellectuals. Now Parikh and Wilczek say their new derivation of Hawking radiation closes the gap1.

That 'pictorial' recipe for how to escape from a black hole goes something like this:

First, empty space is not empty. Quantum physics allows pairs of particles and their antiparticles to be continually created — as long as they go on to annihilate each other a short time later.

Now create a particle–antiparticle pair just past a black hole's doorstep. In the everyday world of 'classical' physics, both particles would be trapped inside.

But quantum physics says there is a chance of one of the particles cheating, by 'tunnelling' its way out.

Wait — if one of the particles tunnels out of the black hole, the pair can't annihilate each other. We're left with a brand new particle outside the black hole — created from nothing. Doesn't this violate the basic rule of physics that there's no such thing as a free lunch?

No, says the theory. The 'created' energy of the escaped particle is made up by a loss of energy from the black hole. Effectively, the black hole has 'radiated' some energy, in the shape of the escaped particle. It works the same way for light as for particles — after all, they're the same thing, according to E=mc2.

What Parikh and Wilczek now show is how this 'quantum tunnelling' picture of Hawking radiation can be derived mathematically. The trick, they claim, is to use a new 'space–time geometry', a new type of 'coordinate system'. This way the edge of the black hole doesn't scupper the equations.

Gary Gibbons of Cambridge University, UK, who worked with Hawking on the original theory, is not completely convinced. "It's unclear how general their argument is," he says. "What happens if the coordinate system is changed?" And, he says, the claim that the earlier work doesn't clearly point to a 'quantum tunnelling' interpretation is "misleading".

One result obtained by Parikh and Wilczek, for the 'spectrum' of energy emitted by the black hole, differs from Hawking's original predictions. So might there be a way to settle the debate, by observing real Hawking radiation?

Unfortunately, there has been no absolutely confirmed sighting of a real black hole, and Wilczek is not optimistic that there will be. "Probably for the foreseeable future, all work on black-hole radiation is theoretical," he says.

In any case, the best astronomical candidates for real black holes, such as the mysterious object at the centre of our own Galaxy, are very massive. The theory predicts that only small black holes can emit significant Hawking radiation. The bigger the black hole, the less light at the end of the (quantum) tunnel.

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