Capping the length of extra dimensions

Size and age of recently discovered black hole shrinks braneworld

Red alert: Scientists are shrinking branes.

BRANE-SHRINKER This illustration depicts a stellar-mass black hole feeding on stars in an elderly globular cluster in the galaxy NGC 4472, about 50 million light-years from Earth. The existence of this small, elderly black hole puts an upper limit of 3 micrometers on the length of any extra dimension proposed by string theorists and particle physicists, a new study suggests. Felix Mirabel, ESA, NASA

A team of theoretical physicists and astronomers has calculated that any hidden extra dimension beyond our familiar three-dimensional space, a world known in physics parlance as a 3-brane, must be less than 3 micrometers. The researchers base their findings on the recent discovery of one of the smallest and oldest black holes ever found.

The new limit is less than half that of previous limits on the length of an extra dimension, Oleg Gnedin of the University of Michigan in Ann Arbor and his colleagues report in a study posted online June 30 (

Physicists since the 1920s have postulated the existence of dimensions beyond the three of space and one of time. Extra dimensions might explain, for example, why the strong nuclear force is roughly 1040 times stronger than gravity. If the gravitational force spreads or leaks out along an extra dimension, as some versions of string theory suggest, it would be weaker in the observable three-dimensional space.

In basic string theory, which describes subatomic particles as tiny vibrating loops or strands of energy, extra dimensions are far too small to be directly detected by any conceivable experiment. But some versions of string theory allow the possibility of larger dimensions whose presence could be detected by measuring the force of gravity at small distances or from the results of atom-smasher experiments or astrophysical observations (SN: 2/19/2000, p. 122).

“The existence of large extra dimensions seems like an attractive idea in theoretical physics, but they have not revealed themselves in any experiment so far,” Gnedin notes.

Enter the search for small, old black holes. According to a process first proposed by University of Cambridge cosmologist Stephen Hawking in 1974, black holes aren’t truly black—nor are they permanent fixtures of the universe. Instead they evaporate by radiating away energy through a quantum-mechanical process that begins when pairs of elementary particles and their antiparticle, such as electrons and positrons, appear near the black hole’s event horizon—the region inside which particles remain trapped by the hole’s gravity.  

In this process, known as Hawking radiation, one particle disappears inside the horizon while its antiparticle escapes to infinity, with the black hole effectively emitting the second particle. The black hole shrinks as it radiates. Hawking radiation proceeds more rapidly for smaller-mass black holes. Moreover, in one of the leading braneworld models, the extra dimensions dramatically speed up the rate at which the black hole radiates, hastening its demise, notes theorist Igor Klebanov of Princeton University. The larger the extra dimension, the faster the black hole evaporates.

Two years ago, astronomers reported evidence for a stellar-mass black hole, most likely only about 10 times as heavy as the sun, in an ancient, tightly packed grouping of stars in the galaxy NGC 4472, some 50 million light-years from Earth. The cluster — and the black hole it contains — is at least 10 billion years old, researchers have estimated.

The very existence of this small, elderly black hole suggests that any extra dimension cannot exceed 3 micrometers in length, the researchers calculate.
Astronomical observations of black holes, such as this one, can give stronger limits than current laboratory tests, Gnedin notes. Perhaps the best physicists and astronomers can do is put limits on the size of extra dimensions, he says. “Beyond that it may be impossible to rule them out.”

Klebanov says of the team’s result: “I think it’s very plausible.”

But Paul Steinhardt of Princeton University cautions, and Gnedin agrees, that the details of the new limit depend on exactly which model for extra dimensions scientists rely on.

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