Black Holes on a String in the Fifth Dimension

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The Fifth Dimension is a very strange place, if one happens to be a physicist and not, say, a popular singing group from the 1960s. Last October an intriguing paper appeared on the arXiv regarding new computer simulations of what happens mathematically to black holes when you analyze them in five dimensions — assuming that the fifth dimension is “compactified.”

Let’s take a closer look at what we mean by a “fifth dimension.” The notion dates back to an early 20th century attempt to unify gravity and electromagnetism. Albert Einstein’s theory of relativity unified three-dimensional space with the fourth dimension of time, and merged gravity and acceleration, attributing the force of gravity to the warping of the fabric of space-time.

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Inspired by Einstein’s work, in 1919, a Polish mathematician named Theodr Kaluza proposed that electromagnetism might be due to a similar warping of an unseen fifth spatial dimension. By reworking Einstein’s equations in five dimensions (four spatial, one temporal), Kaluza believed that he could merge the two forces. He envisioned light as a disturbance caused by the rippling of the higher dimension just beyond human perception, much as fish in a pond can only see the shadows of the ripples across the water’s surface caused by raindrops.

Okay, so what is this compactification nonsense? Well, Kaluza’s theory raised an obvious question: if there is a fifth dimension, why can’t we see it?

Enter Oskar Klein, a Swedish mathematician who argued that this hypothetical fifth dimension could simply be so tiny that not even atoms that could pass into it. Specifically, it would have to be curled up (“compactified”) into a tiny ball much, much smaller than an atom.

String theorists adapted these “Kaluza-Klein models” in the 1970s. According to string theory, there are the three full-sized spatial dimensions we experience every day, one dimension of time, and six extra dimensions crumpled up at the Planck scale like itty-bitty wads of paper.

Yeah. String theory is really complicated like that. Suddenly, blacks holes in five dimensions seem quite manageable, don’t they?

So, this new paper looks at what happens to black holes in five dimensions, where the fifth dimension is compactified. Luis Lehner and Frans Pretorius built on earlier work by Ruth Gregory and Raymond LaFlamme, who found that if you have a black hole in that particular configuration, you would get a “black string” shaped like a cylinder stretched across the extra dimension.

That extra dimension can be larger or smaller than the black hole; the Gregory/LaFlamme model focused on the former scenario, which would give rise to an unstable configuration in the form of “wiggles” in the black string. Here’s the really cool part: those wiggles would eventually cause the string to pinch off into a series of ever-smaller black holes.

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Lehner and Pretorius analyzed this decay of a long black string into multiple black holes all the way to the point where the string shrinks to nothing, until it violates the so-called “cosmic censorship” conjecture that forbids a “naked singularity.” If naked singularities do exist, many believe that this innate “cosmic censorship” would shield them from direct observation.

See, these hypothetical cylindrical black strings have singularities at their center. And if this new analysis is correct — and let’s face it, that won’t be determined experimentally any time soon, seeing as how we haven’t yet observed any evidence for compactified extra dimensions — then cosmic censorship would be violated. As a black string gets smaller and smaller, dividing into multiple black holes, at the moment it shrinks to nothing, its singularity should become “naked” — observable to the outside world.

Did I mention this process is fractal to boot? I’ll let Sean Carroll over at Cosmic Variance explain:

The cool part is the way in which the strings decay into black holes. They form a self-similar pattern along the way — a fractal configuration of black holes of every size, from the largest on down. As the string shrinks in radius, it keeps beading off smaller and smaller black holes. Eventually we would expect them all just to bump into each other and make one big black hole, but the intermediate configuration is complex and elegant. And cosmic censorship is apparently violated when the strings finally shrink to zero radius.

If this all sounds too wacky and far out to be true, consider this: it’s not any weirder than the musical Fifth Dimension’s lyrics in “Age of Aquarius.”

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