SPACE/COSMOS
Tiny black holes: crystals of space and time
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
Vienna University of Technology
image:
Left: visualization of a spacetime-crystel. Right: a cubic crystal structure
view moreCredit: TU Wien
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: tiny 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 Prof. 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.”
Journal
Physical Review Letters
Method of Research
Computational simulation/modeling
Subject of Research
Not applicable
Article Title
Analytic Discrete Self-Similar Solutions of Einstein-Klein-Gordon at Large 𝐷
Astronomers de-fog exoplanet atmospheres with new cloud-detecting method
Discovery by Johns Hopkins researchers of daily cloud cycle on a Hot Jupiter planet provides unique window into its make-up and evolution
Johns Hopkins University
image:
Artistic representation of WASP-94A b, a gas giant in the Microscopium constellation. Clouds build as air flows over the dark side of the planet, reaching a large swell by daybreak. The clouds dissipate on the dayside, leaving clear skies in the early evening.
view moreCredit: Hannah Robbins/Johns Hopkins University
Sand clouds form every morning but clear up by nightfall on WASP-94A b, a well-studied gas giant in a constellation located nearly 700 light years away from Earth.
The research, which uses data from the James Webb Space Telescope (JWST), is among the first to detect cloud cycles on a Hot Jupiter exoplanet. By isolating the clouds, researchers can more accurately measure the planet’s atmosphere and provide one of the clearest pictures to date of the planet’s composition — a significant advance in planetary science.
“I've been looking at exoplanets for 20 years, and general cloudiness has been a thorn in our side. We’ve known for quite a while that clouds are pervasive on Hot Jupiter planets, which is annoying because it’s like trying to look at the planet through a foggy window,” said co-author and program PI, David Sing, a Bloomberg Distinguished Professor of Earth and Planetary Sciences at Johns Hopkins. “Not only have we been able to clear the view, but we can finally pin down what the clouds are made out of and how they’re condensing and evaporating as they move around the planet.”
The results are published today in the journal Science.
To study WASP-94A b in the Microscopium constellation, Sing and his team of researchers gathered data as the planet passed directly in front of its star. Using the high-powered, space-based JWST, the researchers were able to take separate measurements of WASP-94A b's leading edge as it started to cross in front of the star and the trailing edge as the planet completed its transit. At the leading edge, the air flows from the night side of the planet to the day side, effectively making it the morning. Air flows from day to night at the trailing edge, making it the evening.
Observations revealed that mornings and evenings on WASP-94A b have extremely different weather patterns: mornings are riddled with clouds made of magnesium silicate, a common mineral found in rocks, while the evening has clear skies.
The researchers think one of two things could be happening. Powerful winds might lift clouds high into the sky on the cooler side of the planet and then plunge downward on the hotter dayside, dragging the clouds deep into the planet’s interior and effectively burying them out of sight before sunset. Alternatively, the phenomenon may be akin to morning fog burning off on Earth, but on an extreme scale. Clouds would form in the darkness of the planet’s nightside. As they drift into the scorching heat of over 1,000 degrees on the day side, the chemicals that make up the clouds boil away, and the clouds simply vaporize.
“It was a huge surprise. People have expected some differences, like its cooler in the morning than the evening—that’s something natural that we experience here on Earth,” Sing said. “But what we saw was a real dichotomy between the weather on both sides of the planet, and huge differences in cloud coverage, and that changes our whole picture of the planet.”
Because the evenings are clear of clouds, the researchers could look to the trailing edge specifically to see what the atmosphere of the planet looked like—something the Hubble telescope could not provide.
“With the Hubble telescope, when we used to do this type of observation, we got an average view of the whole planet with data from the clouds and the atmosphere squished together and indistinguishable,” said first author Sagnick Mukherjee, a postdoctoral fellow at Arizona State University who was a student at Johns Hopkins and UC Santa Cruz at the time of the research. “This approach with the JWST lets us localize our observations, which helped us see the cloud cycle.”
When the researchers looked at the clear evening sky, they found that WASP-94A b was much more like Jupiter than they thought. Previously, when the clouds were averaged in, the data suggested the planet was made of hundreds of times more oxygen and carbon than Jupiter—a finding that baffled researchers given it couldn’t be explained by planet formation theory. The new data, however, shows WASP-94A b has only five times the amount of oxygen and carbon.
Hot Jupiter planets orbit much closer to their stars—closer even than Mercury to the sun—and therefore are much hotter and are exposed to more radiation. Because of their extreme environments, these planets also make good laboratories to study the chemistry and physics of cloud dynamics.
Using WASP-94 Ab as a benchmark, the team looked at eight other hot gas giants and discovered the same distinctive cloud cycle on two other worlds: WASP-39 b and WASP-17 b. Next, Sing and his team will be using data from a new large JWST program to study cloud cycling across a wide variety of exoplanets, including an eccentric gas giant planet in the habitable zone.
Journal
Science
Article Title
Cloudy mornings and clear evenings on a gas giant exoplanet
Article Publication Date
21-May-2026
Related News Releases
- Astronomers de-fog exoplanet atmospheres with new cloud-detecting method
(Johns Hopkins University)
Different meteorites, same birthplace
The parent bodies of different meteorites may have formed in the same region of the Solar System, as indicated by new computer simulations
Max Planck Institute for Solar System Research
image:
Just outside Jupiter’s orbit, a ring-shaped region of high gas pressure formed. In this “dust trap,” over several million years planetesimals of varying compositions were able to form.
view moreCredit: MPS / hormesdesign.de
When the Solar System formed, a disk of gas and dust orbited the young Sun. Over the course of millions of years, the dust gradually clumped together to form kilometre-sized chunks known as planetesimals. Some grew into planets, while the rest are considered to be the precursors of today’s asteroids. Researchers assume that this development did not proceed in a linear fashion, with different stages of planetesimal development occurring simultaneously, and not every region of the disk offering favourable 'starting conditions' for planetesimals.
In their current study, published today in the journal The Astrophysical Journal, researchers at the Max Planck Institute for Solar System Research (MPS) in Germany identify the ring-shaped region just outside Jupiter’s orbit as not only an efficient, but also a 'pluripotent' planetesimal breeding ground. Computer simulations show for the first time that over the course of two million years, planetesimals with very different compositions formed there.
“Different types of planetesimals apparently formed in the same region of the early dust and gas disk, only at different times. The region just outside Jupiter’s orbit offered excellent conditions for this, said Joanna Drążkowska, head of the Lise Meitner Group on planet formation.
The researchers focused specifically on the period between approximately two and four million years after the birth of the Solar System. By this time, Jupiter had already accreted all the matter in its vicinity, carving a gap in the gas and dust disk along its orbit. According to the current understanding, a ring-shaped region of elevated gas pressure formed just outside its orbit. This led to the accumulation of so much dust, that it coalesced into small clumps of matter, known as pebbles. It was already known that pebbles could grow into planetesimals in such a dust trap at a very early stage. However, it was unclear whether over long periods of time this process could produce bodies with very different compositions. The new study shows that diverse populations of planetesimals can form in dust traps over millions of years. The results thus establish a connection to specific groups of meteorites for the first time. “For the first time, we have succeeded in accurately reproducing the results of laboratory studies of meteorites using computer simulations of the early Solar System. The meteorites serve, so to speak, as a touchstone for theories of planetary formation”, said MPS Director and cosmochemist Thorsten Kleine.
Meteorites are chunks of rock from space that have crashed onto Earth. Most of them are fragments of planetesimals and have hardly changed since they formed. Carbonaceous chondrites, stony meteorites that are particularly rich in carbon, are likely to have formed outside Jupiter’s orbit precisely during the simulated time period, as laboratory studies suggest. Based on age and composition, researchers distinguish six groups of carbonaceous chondrites. While some consist almost exclusively of fine-grained material and crumble apart at the slightest touch, others are significantly more robust. Embedded in the fine-grained material, they contain inclusions that are visible to the naked eye in varying proportions.
In their simulations, the researchers were able to reproduce the age and composition of the six groups of carbonaceous chondrites. In the calculations, the fine-grained material and the inclusions correspond to two types of material that existed in the early Solar System: fragile, crumbly dust and small clumps of more stable material. The latter had formed at the beginning of the Solar System in some places under the influence of heat and then dispersed.
“For our simulations, it was crucial to model the behavior and interaction of both materials on both small and large scales", said Nerea Gurrutxaga, PhD student at the MPS and first author of the paper.
The models therefore take into account the collisions of individual particles (and, as a result, their breaking apart or sticking together) as well as their movements and concentrations within the entire, vast gas disk. For example, both types of particles are drawn from the outer Solar System towards the Sun, albeit at different speeds. Jupiter’s orbit acts as a more effective barrier for the larger, more stable particles than for the smaller dust. The formation of the first planetesimals also consumes some of the available material.
Over time, as a result of all these effects, both types of matter accumulate in varying proportions in the region outside Jupiter’s orbit, thus creating the conditions for the formation of clearly distinguishable generations of planetesimals. In the first 500,000 years, the proportion of crumbly material initially decreases, only to increase over the next million years.
Thereafter, two distinct populations of planetesimals emerge, consisting either almost exclusively of crumbly material or stable material.
Based on their calculations, the researchers believe that, at an earlier stage, meteorite types other than carbonaceous chondrites may also have formed in the dust trap beyond Jupiter. 'There is strong evidence that dust traps were the preferred birthplace of planetesimals in our Solar System,' says Joanna Drążkowska.
... Others, such as the Ivuna meteorite, consist almost entirely of fine-grained, crumbly material. The capsule shown here is only about one centimeter long and contains a few grains of this very rare meteorite.
Carbonaceous chondrites can look very different. Some, such as the Allende meteorite shown here, contain a high proportion of clearly recognizable inclusions. …
Credit
MPS / T. Klawunn
Different groups of carbonaceous chondrites (here CO, CV, CM, TL, CI, and CR) can be traced back to different generations of planetesimals that formed over the course of about two million years. They differ in their proportions of fine-grained material (shown here in blue) and inclusions (shown here in brown).
Credit
MPS / hormesdesign.de
Journal
The Astrophysical Journal
Method of Research
Computational simulation/modeling
Subject of Research
Not applicable
Article Title
Carbonaceous Chondrites provide evidence for late-stage planetesimal formation in a pressure bump,
Article Publication Date
22-May-2026
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