A research team from Vienna and Frankfurt has discovered a mathematical formula for a bizarre phenomenon: space and time can form a crystal-like structure capable of transforming into a black hole.
Black holes usually originate from spectacular cosmic events. The death of a massive star is the most common example. However, physics dictates that arbitrarily small black holes are also theoretically possible. These microscopic objects can emerge from specific critical states stimulated by tiny amounts of energy.
Such states likely existed shortly after the Big Bang when the universe was a chaotic mixture of particles. These environments could have birthed primordial black holes. Computer simulations confirmed the possibility of these critical structures decades ago. Now, a team from Goethe University Frankfurt and TU Wien has used an unusual mathematical trick to prove this phenomenon with an exact formula.
Freezing Spacetime
“Sometimes a small, unspectacular cause is enough to trigger a large, spectacular change,” explains Daniel Grumiller from TU Wien. “Imagine liquid water at zero degrees Celsius. A microscopic change is enough to make the water freeze. The water molecules spontaneously arrange themselves into a regular pattern to form an ice crystal.”
According to Albert Einstein’s Theory of General Relativity, a remarkably similar process can happen to space and time. When particles move through space, they interact with their environment.
“We say that spacetime is curved by mass,” says Christian Ecker from the Institute for Theoretical Physics at Goethe University Frankfurt. “Large objects like stars curve spacetime intensely, which we can observe when starlight bends around them. However, smaller masses also cause spacetime curvature to a lesser extent.”
Just as thermodynamics allows water molecules to transition from disordered liquid into a structured crystal, relativity allows spacetime curvatures to form a recurring pattern in space and time. This creates a “spacetime crystal.” Physicists refer to the transition leading to this state as a critical collapse.
A Gateway to Black Holes
“This spacetime crystal is a highly unusual and peculiar object,” Grumiller says. “It acts as an intermediate state—an unstable tipping point that can evolve in two completely different directions. It can simply decay back into ordinary spacetime with scattering particles. However, if you add a minimal amount of energy, the evolution takes a radical turn: the inconspicuous spacetime crystal collapses into a black hole.”
[ Spacetime Crystal ]
(Unstable State)
|
+---------------+---------------+
| |
(Decays naturally) (Add minimal energy)
v v
[ Ordinary Spacetime ] [ Black Hole ]
Computer simulations from 1993 first suggested that black holes could form spontaneously this way. Since then, scientists have tried to describe this process mathematically and derive the exact formulas. The task proved to be incredibly difficult until the Austro-German team utilized a baffling shortcut.
The Trick of Infinite Dimensions
“Our universe has four dimensions: three spatial dimensions and one time dimension,” Christian Ecker explains. “In principle, however, nothing stops us from writing down physical equations for a higher number of dimensions—whether it is five, forty-two, or even infinitely many.”
One might assume that adding dimensions makes the theory exponentially more complex, but the opposite is true. The team demonstrated that in the limiting case of infinite dimensions, highly complex mathematical questions become surprisingly easy to answer.
Once the solution is found in the infinite-dimensional space, the physicists “reverse-translate” the results back to fewer dimensions. By taking a detour through a hypothetical, infinite-dimensional world, the team unlocked critical insights into our own four-dimensional reality.
“Our technique proves to be highly stable. Depending on the required precision, we can even improve our formulas using additional approximation methods,” says Florian Ecker from TU Wien. “We have developed a method that allows us to analyze phenomena surrounding black holes that were previously considered impossible to calculate.”
Sources:
- TU Wien
- Goethe University Frankfurt
