You already know that water freezes. At zero degrees, the disordered chaos of liquid molecules suddenly snaps into a regular, repeating pattern into an ice crystal, through a process physicists call a phase transition. It is one of the most familiar things in nature. What is considerably less familiar is the idea that space and time can do exactly the same thing and when they do, what emerges is not ice, it’s a black hole.

A close up of ice crystals displaying typical hexagonal symmetry (Credit : Maxim Bilovitskiy)

It may seem like it but this is not science fiction, it’s the conclusion of a new study published in Physical Review Letters by researchers from TU Wien in Vienna and Goethe University Frankfurt. They have for the first time, derived an exact mathematical formula describing one of these strange theoretical objects in physics and they’re known as a spacetime crystal.

Black holes, as most people understand them, form in violence. A massive star runs out of fuel, its core collapses under its own gravity, and the result is an object so dense that not even light can escape. But Einstein's theory of relativity allows for something altogether more subtle, namely microscopic black holes. These emerge not from catastrophic collapse but from a delicate critical state, a moment of perfect balance in which spacetime organises itself into a structured, repeating pattern before tipping, with the addition of the tiniest amount of energy, into a black hole.

Imagine holding water at exactly zero degrees, right on the boundary between liquid and solid. In that critical state, the slightest nudge determines everything. A fraction of a degree colder and you get ice, a fraction warmer and you get water and the spacetime crystal sits at exactly this kind of boundary. Left alone it dissolves back into ordinary spacetime. Add the smallest amount of energy and the whole structure collapses into a black hole. The process that creates it is called critical collapse, and it is one of the most intriguing phenomena in theoretical physics.

"Our technique turns out to be remarkably stable. This gives us a new method for studying black hole related phenomena that could previously not be analysed analytically" says Florian Ecker from TU Wien.

Computer simulations had already suggested this was possible back in 1993 but in thirty years, nobody had managed to describe it with an exact mathematical formula. The equations turned out to be really quite difficult until the Vienna and Frankfurt team found a trick that nobody had tried before.

Rather than solving the problem in our familiar four dimensions of space and time, they solved it in infinitely many dimensions instead! Wait, what?? This sounds like it should make things harder but remarkably, it makes them easier. In the limit of infinitely many dimensions, certain mathematical complexities that make the problem intractable in four dimensions simply vanish. Once the solution exists in infinite dimensions, it can be carefully translated back to the universe we actually live in.

Source : Tiny black holes: crystals of space and time