Mining black holes

Here’s something that boggled my mind, and which I wrote up for BBC Future.

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It’s a staple of science fiction: highly advanced civilizations getting their energy by mining black holes, extracting it from collapsed stars or making artificial mini-holes that power spaceships. These aren’t idle or quasi-magical speculations, for physicists have believed for at least 30 years that it might be possible. However, sci-fi writers wishing to draw on this technological miracle are going to have to get more inventive, for a paper published in the premier physics journal Physical Review Letters now argues that mining black holes would not be as productive as was thought.

The classical view of black holes as stars that have burnt out and collapsed under their own gravity to an infinitesimally small point in space – a singularity – offered little prospect that they were anything other than dead, barren light traps. Inside the so-called event horizon around the hole’s absurdly dense centre, nothing can escape from the hole’s gravity, and it just sits there forever like a blot on spacetime.

But that changed once Stephen Hawking and others brought quantum physics to bear on this picture. Hawking showed in the 1970s that black holes don’t last forever, and that to the world outside the event horizon they are not black at all. He argued that black holes emit energy from their boundaries in the form of radiation produced by quantum fluctuations of empty space itself. Eventually this Hawking radiation leads to evaporation of the black hole itself.

That happens so slowly that black holes with the mass of a star are still hardly less than eternal. But might it be possible to induce a black hole to release all its Hawking radiation sooner, so that in effect it becomes like a ball of fuel? In 1983 physicists George Unruh and Robert Wald suggested how to do that. One could lower a box down close to the hole’s event horizon, let it fill up with Hawking radiation, and then bring it back up again, just like filling a bucket with water from a well. Performed repeatedly, this manoeuvre would gradually strip the black hole of its ‘hot atmosphere’ of radiation. True, you’d need a mighty rope and winding mechanism to prevent the box from being tugged beyond the event horizon and swallowed, but in principle it could be done.

Or can it? Adam Brown of the Princeton Center for Theoretical Science says that it would take far longer than Unruh and Wald anticipated. He shows that the attempt would cause the black hole to swell and engulf the box. “Rather than using the box to rob the black hole of its radiation”, he writes, “the black hole instead robs us of our box.”

The problem, says Brown, lies with the plain old mechanics of the rope holding the box. Because it would be in a gravitational field, the rope would be subject to the inevitable constraint that it can’t be heavier than its own strength can support. This is true even for exotic ‘ropes’ that aren’t material at all, such as electric or magnetic fields: they too have an energy density and thus (via E=mc**2) an effective mass.

For an ordinary rope hanging down in the Earth’s gravity, the tension in the rope increases with height, because it is carrying more of its own weight. But weirdly, in a very strong gravitational field, where spacetime itself is highly curved, the tension remains the same all along the length. However, for the rope to be stable, it turns out that this tension must exactly equal the mass per unit length of the rope: the rope has to be in effect at breaking point purely to support its own weight, so that there is no strength left over to support the box that will collect Hawking radiation.

Another constraint on the rope is that it mustn’t disintegrate. Close to a black hole, the intense Hawking radiation creates a hot environment. If the rope is lowered too close to the event horizon, where the radiation is most plentiful, there’s a danger that the temperature will exceed that at which all ordinary matter – in other words, atoms themselves – melt into a gloop of their constituent quarks. If you make the rope too light, it’s more likely to melt. But if you make it too heavy, the rope itself is in danger of collapsing under its own gravity.

There’s another complication too. Brown shows that the box itself can’t be wider than a single wavelength of the Hawking radiation it is collecting, since otherwise the effects of relativity will pull it awry and cause the rope to break. That would make the collection process very cumbersome in any case – it would have to happen one photon (‘light particle’) at a time. To collect Hawking radiation of the wavelength of light, the boxes could be no bigger than typical bacteria, and to collect X-rays you’d need atom-sized boxes.

So here’s the deal. If you get too close to the black hole, the rope might melt or snap – or, if it’s made too massive to avoid that, it might collapse into itself. But if you try mining at a more cautious distance, there isn’t so much Hawking radiation there to collect. And Brown shows that even the best compromise makes energy extraction much slower than Unruh and Wald suggested.

Yet there is a better way, he says: do away with boxes altogether. In 1994, Albion Lawrence and Emil Martinec of the University of Chicago proposed that one could simply dip strings into a black hole and let Hawking radiation run up them like oil up the wick of an oil lamp. This was thought to be a slower process than hauling up boxes full of Hawking radiation, because each string carries up only one photon at a time. But Brown’s analysis shows that they would in fact both mine the hole at the same (slow) rate. Since dangling boxes introduce more potential for malfunction, Brown therefore argues that the preferable way to draw the energy from black holes is to puncture the event horizon with lots of photon-wicking strings, and let them drain it out of existence.

Reference: A. R. Brown, Physical Review Letters 111, 211301 (2013)