Left: visualization of a space-time-crystal. Right: a cubic crystal structure
Image Credit: Technische Universität Wien
Scientific Frontline: Extended "At a Glance" Summary: Spacetime Crystals and Microscopic Black Holes
The Core Concept: Researchers have developed an exact mathematical formula describing how arbitrarily small, microscopic black holes can spontaneously form from highly ordered, unstable states known as spacetime crystals.
Key Distinction/Mechanism: Unlike massive black holes formed by the collapse of dying stars, these microscopic black holes emerge through "critical collapse." Spacetime curvature temporarily organizes into a regular, repeating pattern (a spacetime crystal)—an intermediate state that either dissolves or, with the slightest addition of energy, collapses into a tiny black hole.
Origin/History: The possibility of spontaneous microscopic black hole formation was first observed in computer simulations in 1993. It was only recently confirmed analytically, using paper-and-pencil mathematics, by physicists at TU Wien and Goethe University Frankfurt.
Major Frameworks/Components:
- General Relativity: Albert Einstein’s foundational framework establishing that mass and particle movement cause spacetime curvature.
- Critical Collapse: A phase-transition process where disordered spacetime organizes into a regular structure, analogous to liquid water freezing into an ice crystal.
- Infinite-Dimensional Mathematics: An unconventional mathematical trick where physicists solve equations by assuming an infinite number of dimensions (where complex problems simplify) and then approximate the results back into our four-dimensional universe.
Branch of Science: Theoretical Physics, Astrophysics, and Cosmology.
Future Application: The novel "infinite dimension" mathematical technique developed for this proof provides a stable, systematic toolkit for scientists to study complex black-hole-related phenomena that were previously impossible to solve analytically.
Why It Matters: This mathematical proof bridges a 30-year gap between computer models and fundamental physics, offering vital insights into the primordial black holes that may have formed from the chaotic particle mixtures shortly after the Big Bang.
A team from Vienna and Frankfurt has found a formula describing a strange phenomenon: space and time can form a kind of “crystal” that may turn into a black hole.
Alongside the famous gigantic black holes, physics also allows for microscopic versions. They emerge from so-called critical states when spacetime organizes itself into a regular, crystal-like structure during a process known as critical collapse. A team from Goethe University Frankfurt and TU Wien has now succeeded, for the first time, in describing this phenomenon with an exact mathematical formula using an unusual mathematical trick.
Black holes usually form in spectacular events, such as the death of a massive star. But in theory, arbitrarily small black holes are also possible: microscopic objects that can emerge from special critical states after the slightest addition of energy. Such states may have existed shortly after the Big Bang, when the universe was still a chaotic mixture of particles, potentially giving rise to so-called primordial black holes.
The theoretical possibility of such critical structures had already been demonstrated in computer simulations. Now, researchers from Goethe University Frankfurt and TU Wien have managed to confirm these results with a mathematical formula—using nothing more than paper and pencil.
Critical Collapse
“Sometimes a tiny, seemingly insignificant cause is enough to trigger a huge and dramatic change,” says Professor Daniel Grumiller from TU Wien. “Take liquid water at zero degrees Celsius, for example. A very small change is enough to make the water freeze. The water molecules then spontaneously arrange themselves into a regular pattern and form an ice crystal.”
According to Albert Einstein’s theory of relativity, something very similar can happen in space and time. Whenever particles move from one place to another, they affect spacetime itself. “We say that spacetime is curved by mass,” explains Christian Ecker from the Institute for Theoretical Physics at Goethe University Frankfurt. “Large objects such as stars curve spacetime strongly—for example, we can observe this when light rays are deflected by massive stars. But smaller masses also produce spacetime curvature, just to a lesser extent.”
Just as physics allows water molecules to form a regular crystal out of disordered liquid water, relativity allows spacetime curvature to organize itself into a regular structure—a repeating pattern in space and time. A kind of “spacetime crystal” emerges. Physicists refer to the process leading to this state as critical collapse.
“This spacetime crystal is a very peculiar and fascinating object,” says Grumiller. “It is a kind of intermediate state, an unstable point that can evolve in two different directions. It may simply dissolve again, leaving behind ordinary spacetime filled with freely moving particles. But if a tiny amount of energy is added, the evolution takes a completely different path: the inconspicuous spacetime crystal turns into a black hole.”
Confirming an Old Hypothesis
Computer simulations had already suggested back in 1993 that black holes might form spontaneously in this way. Since then, researchers have tried to describe the process mathematically and derive the correct formulas—but this turned out to be extremely difficult. The team from Vienna and Frankfurt has now solved the problem using a remarkable trick.
“Our universe has four dimensions—three dimensions of space and one dimension of time,” explains Christian Ecker. “But in principle, nothing prevents us from writing down physical equations for a larger number of dimensions—five dimensions, forty-two dimensions, or even infinitely many.”
One might expect the theory to become vastly more complicated that way, but that is not necessarily the case. The team showed that, in the limit of infinitely many dimensions, some highly complex questions become surprisingly simple. The next step is to check whether the solution can be translated back to a smaller number of dimensions. In this way, the researchers were able to gain insights into our four-dimensional universe by taking a detour through a hypothetical universe with infinitely many dimensions.
“Our technique turns out to be remarkably stable. Depending on the desired precision, we can systematically improve our formulas using additional approximation methods,” says Florian Ecker from TU Wien. “This gives us a new method for studying black-hole-related phenomena that could previously not be analyzed analytically.”
Published in journal: Physical Review Letters
Title: Analytic Discrete Self-Similar Solutions of Einstein-Klein-Gordon at Large 𝐷
Authors: Christian Ecker, Florian Ecker, and Daniel Grumiller
Source/Credit: Technische Universität Wien
Edited by: Scientific Frontline
Reference Number: phy052126_01