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Holes in one

Despite their fearsome reputation, not all black holes are cosmos-gobbling monsters, says Marcus Chown. There could even be one inside you

CAUGHT in a high-tech trap, a lone atom is blinking. From the spectrum of its light it looks like a cadmium atom. But to the scientists who have trapped it, there's something not quite right: the frequency is shifted by a puzzling 0·002 per cent. Their unease gives way to astonishment as they discover that their captive is a billion billion times heavier than an ordinary atom. Staring them in the face is a freak of nature--for in place of a nucleus, this atom has a gaping hole. A black hole.

According to Victor Flambaum and Julian Berengut of the University of New South Wales in Sydney, black hole atoms such as this are a real possibility. In a paper submitted to Physical Review A, the two physicists have calculated the bizarre properties of these objects. Black hole atoms could be part of the dark matter that binds the Galaxy, they might accelerate nuclear reactions in stars, and they could tell us about conditions in the first fraction of a second of the life of the Universe. Strangest of all, there could be black holes inside you, and you wouldn't even notice.

In an ordinary atom, negatively charged electrons orbit positively charged protons and uncharged neutrons, which are clumped into a tiny nucleus 1/100 000th the diameter of the atom. There is no reason why this central positive charge could not be provided by something else, as long as it is small enough. But how could black holes fit the bill?

Astronomers have detected several black holes in our Galaxy, the relics of massive stars which gravity has crushed out of existence (see page 28). These holes weigh several times as much as the Sun, and are a few kilometres across--hardly a handy size to slip inside an atom. Even less suitable are the colossal black holes with billions of times the mass of the Sun that power quasars (see page 32). But theorists think that microscopic black holes might have been squeezed into existence in the first split second after the big bang. It is these that could form the kernels of black hole atoms.

To make an atom, a primordial black hole would have to carry a positive electrical charge, just as a nucleus does. Flambaum says that black holes are more likely to be charged than not. "They get their charge simply by swallowing charged particles," he says. "It could be negative or positive, depending on what they swallow."

But to make a substitute nucleus, a black hole must also be stable--which microscopic black holes aren't supposed to be. In 1971, the Cambridge University physicist Stephen Hawking showed that black holes radiate subatomic particles, causing them to slowly evaporate away. As the hole becomes smaller, the sleet of particles becomes a ferocious blizzard, until the last shred of the black hole vanishes in a blast of radiation. On the face of it, this spells death to any black hole atom. However, Flambaum and Berengut reckon that Hawking's evaporation could eventually stop, leaving a tiny, long-lived black hole behind.

Jacob Beckenstein discovered in 1995 that the area of a black hole's event horizon--the boundary which marks the point of no return for in-falling matter--is quantised. In other words, it can only have certain discrete values. As a hole evaporates, its area, and therefore its mass, falls step by step. By the time it has only a few quanta of horizon area left, Hawking's calculations break down. No one can work out exactly what should happen, but many physicists think the black hole might stop evaporating altogether, or at least hang around for many billions of years before evaporating. To conserve such physical quantities as charge and angular momentum, the residual black hole would have to turn into a collection of particles with very particular properties--something that quantum mechanics makes highly improbable.

If so, the Universe could be awash with charged primordial black holes of about a Planck mass, or 0·00001 grams. They would have an incredibly tiny radius of 10-35 metres. And in the aeons they have been drifting through the gas of interstellar space, they would have gathered about them a cloud of electrons to neutralise their positive charge. "The electrons would orbit just like in a normal atom," says Flambaum.


If such a beast were to run into the Earth, it could get trapped on the surface and become lodged in a rock, in a laboratory bench, or even in your head. What would this super-atom be like?

At first glance, there appears to be no limit to the number of orbiting electrons a black hole atom can have--it should depend merely on the charge of the black hole. It is easy to imagine atoms with a thousand electrons, or a million. But it turns out that there are limits: a fundamental one, and a practical one set by the age of the Universe.

The fundamental limit was discovered by the British physicist Paul Dirac. He knew that in a normal atom, an electron is prevented from spiralling into the nucleus by Heisenberg's uncertainty principle. Electrons are attracted by the positive charge on the nucleus, but any electron trying to orbit too close to the nucleus would be stuck in a very confined space. According to the uncertainty principle that means it would have to move very fast, too fast to be trapped there by the electrical attraction of the nucleus.

But if the nucleus has a very large charge, the increased pull would be enough to overwhelm the uncertainty principle. "Dirac found that for an atom with more than 137 electrons there are no stable electron orbits," says Flambaum. "All electrons spiral down to nuclear oblivion."

So any charged black holes that formed in the big bang could not have collected more than 137 electrons. Any surplus would have been swallowed by the hole almost instantly, cancelling out part of its positive electrical charge.

But that's not the only constraint. Any hole that started out with a charge as high as 137 would be less charged by now, because it turns out that electrons don't have to spiral in to be gobbled up. An electron isn't a discrete little ball: its existence is actually smeared out. This means that a small part of the existence is always within the black hole's horizon, which translates into a small probability that the electron will be swallowed. This probability increases with the cube of the charge on the hole. So highly charged black hole atoms quickly polish off their inner electrons. According to Flambaum, the most complex black hole atoms that we could expect to see in today's Universe would have 70 electrons, corresponding to the element ytterbium.

If experimenters were to trap a black hole atom in their lab, what would it look like? The wavelength of light emitted by a normal atom depends on the energy levels that its electrons can occupy. These are affected slightly by the motion of the nucleus: a nucleus moves a little as a result of the pull of an electron orbiting it, just as the Sun wobbles slightly under the influence of the Earth's gravity. The effect in an ordinary atom is to shift the wavelength by a tiny amount from what it would be if the nucleus were immovable--that is, if its mass were infinite. "But a Planck mass black hole is effectively an infinite mass," says Flambaum. "So you wouldn't get the shift you get for a normal atom. Such a difference would be easy to see with modern instruments."

A more dramatic effect would occur if an inner electron was gobbled. Then the black hole atom would do a quick change. A cadmium black hole atom with 48 electrons would spontaneously turn into a silver black hole atom with 47 electrons. And as the hole's mass depends on its charge, such a transformation would produce a huge burst of radiation.

So what are the odds of detecting a black hole atom, either in space or on Earth? It really depends on how many of them are kicking around the Universe. We can get a rough idea of the maximum possible number by postulating that the Universe's invisible "dark matter" is made entirely of black hole atoms. "At best we could hope for one black hole atom for every 1000 trillion trillion hydrogen atoms," says Flambaum. "That would make them about 30 times rarer than uranium atoms."

So there is no doubt that black hole atoms would be rare creatures, but Flambaum's point is that they might not be impossibly rare. He suggests that the best bet could be to look for their anomalous spectral lines in gas around the Sun. The real problem in detecting one would be in spotting its light amid the blaze of light from countless normal atoms. Flambaum admits that this would be quite a challenge.

Exotic entities

Atoms with a positively-charged black hole in their hearts may seem weird. But Flambaum and Berengut have imagined some even more exotic entities, formed when a minimum-mass black hole has a negative charge. "Instead of gathering electrons about it as it travelled through space, it could gather protons or even nuclei," says Flambaum. Such a "protonic" atom would be about 2000 times smaller than a normal atom--so small that short-range nuclear forces would come into play. Two protons in orbit around a hole would react to form a deuterium nucleus. Such a reaction, which is the first step in the process of making sunlight, takes about 10 billion years to happen in the Sun. However, it would happen much faster around a black hole, where the two protons are close enough for nuclear forces to snap them together.

The arrival of a third proton would trigger the nuclear reaction to make helium-3, and the process carry on to build ever heavier nuclei around the black hole. Flambaum and Berengut point out that the nuclei would be very different from normal nuclei, which have to contain large numbers of neutrons to glue them together because of the tremendous electrical repulsion between protons. But around a black hole, the protons would be squeezed together by the hole's gravity. "Consequently, you would expect nuclei far richer in protons than normal nuclei," says Flambaum. This type of black hole atom could act as a catalyst for building new elements in stars. The energy released in the reaction could make a nucleus fly off, allowing new protons to be captured.

Another, weirder possibility, arises because a proton is a very large object compared with a point-like black hole. From the point of view of the hole, a proton is not a single object but an assembly of three quarks. "This means that there is the possibility of the proton actually losing one of its quarks to the black hole," says Flambaum. The black hole would then possess colour charge, a property thought to be the preserve of quarks alone. In effect it would become a superheavy quark, and from a distance the whole system of two quarks orbiting a quark black hole would appear to be a superheavy proton. If we could cap- ture these weird particles they would make a great test bed for theories of how quarks interact with each other. The snag is that they'd be very hard to catch. They are so small that they would fall between the ordinary atoms of a solid and so could never be trapped on the Earth's surface.

But most significantly, black hole atoms might provide a window onto the very early Universe, all the way back to the first instant, within 10-43 seconds of the beginning. This is far earlier than any other relics, such as photons or neutrinos. According to Bernard Carr of Queen Mary and Westfield College in London, primordial black holes would tell us how lumpy the early Universe was. They might even preserve a memory of a time when the fundamental constants of nature were different from their values today. For example, in some cosmological models the strength of gravity varies in the very early Universe. Relic black holes might record this variation in the values of their mass.

So although Flambaum admits that black hole atoms of all types would be very difficult to detect, the rewards could be great. "Looking for them has got to be worth a try," he says. Just don't expect to see black hole paperweights in the shops any time soon.

From New Scientist magazine, 01 April 2000.

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