from the a-topologist-doesn't-know-his-ass-from-a-hole-in-the-ground dept.
In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.
The cosmos seems to have a preference for things that are round. Planets and stars tend to be spheres because gravity pulls clouds of gas and dust toward the center of mass. The same holds for black holes — or, to be more precise, the event horizons of black holes — which must, according to theory, be spherically shaped in a universe with three dimensions of space and one of time.
But do the same restrictions apply if our universe has higher dimensions, as is sometimes postulated — dimensions we cannot see but whose effects are still palpable? In those settings, are other black hole shapes possible?
The answer to the latter question, mathematics tells us, is yes. Over the past two decades, researchers have found occasional exceptions to the rule that confines black holes to a spherical shape.
Now a new paper goes much further, showing in a sweeping mathematical proof that an infinite number of shapes are possible in dimensions five and above. The paper demonstrates that Albert Einstein's equations of general relativity can produce a great variety of exotic-looking, higher-dimensional black holes.
[...] As with so many stories about black holes, this one begins with Stephen Hawking — specifically, with his 1972 proof that the surface of a black hole, at a fixed moment in time, must be a two-dimensional sphere. (While a black hole is a three-dimensional object, its surface has just two spatial dimensions.)
Little thought was given to extending Hawking's theorem until the 1980s and '90s, when enthusiasm grew for string theory — an idea that requires the existence of perhaps 10 or 11 dimensions. Physicists and mathematicians then started to give serious consideration to what these extra dimensions might imply for black hole topology.
[...] In 2002, three decades after Hawking's result, the physicists Roberto Emparan and Harvey Reall — now at the University of Barcelona and the University of Cambridge, respectively — found a highly symmetrical black hole solution to the Einstein equations in five dimensions (four of space plus one of time). Emparan and Reall called this object a "black ring" — a three-dimensional surface with the general contours of a doughnut.
[...] Learning about that result gave hope to Rainone, a topologist, who said, "Our universe would be a boring place if every planet, star and black hole resembled a ball."
[...] Galloway was particularly impressed by the strategy invented by Khuri and Rainone. To prove the existence of a five-dimensional black lens of a given p and q, they first embedded the black hole in a higher-dimensional space-time where its existence was easier to prove, in part because there is more room to move around in. Next, they contracted their space-time to five dimensions while keeping the desired topology intact. "It's a beautiful idea," Galloway said.
The great thing about the procedure that Khuri and Rainone introduced, Kunduri said, "is that it's very general, applying to all possibilities at once."
[...] Meanwhile, an even bigger mystery looms. "Are we really living in a higher-dimensional realm?" Khuri asked. Physicists have predicted that tiny black holes could someday be produced at the Large Hadron Collider or another even higher-energy particle accelerator. If an accelerator-produced black hole could be detected during its brief, fraction-of-a-second lifetime and observed to have nonspherical topology, Khuri said, that would be evidence that our universe has more than three dimensions of space and one of time.
Such a finding could clear up another, somewhat more academic issue. "General relativity," Khuri said, "has traditionally been a four-dimensional theory." In exploring ideas about black holes in dimensions five and above, "we are betting on the fact that general relativity is valid in higher dimensions. If any exotic [nonspherical] black holes are detected, that would tell us our bet was justified."
(Score: 2, Funny) by shrewdsheep on Monday January 30 2023, @01:31PM (2 children)
Does it mean my spherical cows are bulging into hidden dimensions?
(Score: 3, Funny) by Freeman on Monday January 30 2023, @06:19PM
Nope, it means your spherical cow can also be a trapezoid or some weird shape.
Joshua 1:9 "Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee"
(Score: 5, Interesting) by Immerman on Monday January 30 2023, @06:50PM
More like, if they existed, then you could have a toroidal cow that was also a black hole.
Now, granted, all real-life animal are topologically toruses, but they're generally not also black holes, so we can' really draw any conclusions from that fact.
Also, IF the dimensions exist, then *everything* is bulging into them. String theory after all posits that all our fundamental particles are actually energy rings vibrating in all those dimensions. In fact, giving those rings enough freedom to vibrate in the right ways to create in the particles we know of is the *only* reason we have to suspect they might exist at all. All experimental attempts to confirm them have failed. Though in fairness, they may well all loop back on themselves at distances far smaller than an atom, so looking for them is really just looking for an easy win for the apparently otherwise completely unsubstantiatable string theory.