It’s a long-established fact that water freezes. At the freezing point, the disordered molecular chaos of the liquid transforms abruptly into the ordered, repeating pattern of an ice crystal through a process physicists refer to as a phase transition. This is quite common knowledge. Far less understood, however, is the idea that spacetime itself can undergo a similar transition and, when it does, the resulting formation is not ice, but a black hole.
While it may sound like science fiction, it’s actually a conclusion from recent research published in Physical Review Letters by scientists from the Vienna University of Technology and Goethe University Frankfurt. For the first time, they have derived a precise mathematical description for one of these theoretically exotic objects in physics: a spacetime crystal.
Black holes, as most people conceive of them, emerge from a violent process. A massive star exhausts its fuel, its core collapses under its own gravity, and the result is an object so dense that not even light can escape. Einstein’s theory of relativity, however, allows for something far more subtle: microscopic black holes. These don’t arise from catastrophic collapse but rather a delicate critical state, a moment of perfect equilibrium where spacetime organizes itself into a structured, repeating pattern, before, with the addition of the tiniest amount of energy, collapsing into a black hole.
Imagine holding water at precisely zero degrees Celsius, right at the threshold between liquid and solid. In this critical state, the slightest disturbance dictates everything. A fraction of a degree colder, and you get ice; a fraction of a degree warmer, and you get liquid water. The spacetime crystal exists precisely at this boundary. Left undisturbed, it would dissolve back into normal spacetime. Add the smallest bit of energy, and the entire structure collapses into a black hole. The process that forms it is called critical collapse, and it is one of the most intriguing phenomena in theoretical physics.
“Our method turned out to be surprisingly stable. It gives us a new way to study black hole-related phenomena that were not analytically tractable before,” says Florian Ecker from the Vienna University of Technology.
Computer simulations had hinted at this possibility as far back as 1993, but for thirty years, no one managed to describe it with an exact mathematical formula. The equations proved quite complex until the team from Vienna and Frankfurt found an approach no one had tried before.
Instead of tackling the problem in our familiar four dimensions of spacetime, they solved it in an infinite number of dimensions! Wait, what?? This sounds like it should make things harder, but astonishingly, it actually simplifies them. In the limit of infinite dimensions, certain mathematical complexities that make the problem intractable in four dimensions simply vanish. Once a solution exists in infinite dimensions, it can be carefully translated back into the universe we actually inhabit.
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